Trying to figure out if Senior Railcard will save money or hassle

Not entirely sure but think Britrail charge fees.
Check travel on the national rail site ir even the individual rail companies
The Seniors railcard has few limitations ,generally no travel before 9.30 am on weekdays.

I am fond of " split ticket" App too
With that combo of journeys you should easy cover the cost of the Senior railcard

If I am travelling even a week out is enough time to get good fares

Just out of interest how much is a britrail pass,from memory last time I looked there was a fair premium in using one rather than just buying directly.

Railcards are accepted by Lumo, as per their website: https://www.lumo.co.uk/tickets/railcards

They are also usable on London-Windsor & London-Bletchley outside of the morning peak.

Thanks, all.

@Richard, the Senior Railcard cost is £30. The BritRail Pass is considerably more. I was using the britrail.com/map/ only to figure out what journeys would be covered. I can check for savings through splitting the ticket too.

@Marco, thanks for referring me to the Lumo website. I hadn't thought to look there. Also thanks for the information about Windsor and Bletchley. I would leave for those considerably before 9:30, however, so no savings there for me. I hope others can benefit.

You can easily check discount by looking at the fare without card applying then adding the card
Have you had a look at www.seat61.com for information on rail travel in UK?
You should be able to find a London to Edinburgh Advance Single fare just over £20 with rail card discount

Here is a good map of the rail network.

You will find the cheapest fares as Advance specific train tickets (non refundable) which get loaded around 11 weeks out. However, even booking a week or so before travel can still get you reasonable prices. For short hops it is usually best to just pay on the day as booking ahead will make no difference. Not sure why you are going to Holyhead unless to catch a ferry to Dublin. North Wales has wonderful places to visit and Holyhead is not one of them. However, Anglesey has some lovely beaches though inland is mainly flat farmland. Also not sure why you are not stopping for at least 1 night in historic York as it is on the main line from London (Kings Cross) to Edinburgh. (Lumo don’t stop at York).

I suggest you play around with dates on the following sites and see if by inserting the Senior Railcard tick box gets you a better deal. Then compare that with Britrail. https://www.traintickets.com/?/ AND/OR https://www.nationalrail.co.uk

Nancycantravel

If you are going to Holyhead merely to catch a ferry I suggest getting a through rail-sail ticket. From Chester to Dublin that is £40.40 and can be purchased up until the moment of travel.
The ferry fare on it's own is £36.

But if you have time I recommend a few nights in Holyhead. Not for the non descript town itself, but it is the centre of bus services on this large and beautiful island which is too often overlooked.
In particular if you can you should go to South Stack lighthouse. Bus services to there come and go (last time I looked it was suspended indefinetly again), but it is a perfectly manageable walk from Holyhead.
Another unusual sight is the harbour breakwater. It is the longest in the UK at 1.7 miles long and can be walked for it's full length, at it's landward end there is a nature reserve. I accept a breakwater may seem a bit esoteric.
As a rough guide you should get
LKX-EDI for about £30
EDI- GLA £9
GLA-Lanark CDR £5.50
GLA-Liv £9.75 to £14
Liv-Chester £4.15 on Transport for Wales (from Lime Street High Level), £5.60 on Merseyrail (from Lime Street Low Level). TFw are hourly, Merseyrail every 15 minutes
Chester to Holyhead £10
(all railcard fares, advance fares where the route has them),
so say £75, plus your railcard= £105.
All these are actually for 6 weeks time today (4 weeks time for GLA-Liv due to the Carstairs blockade in 6 weeks time) so even lower fares may be attained booking 12 weeks out. But I have gone for realistic.
I believe that is around £150 less than the Britrail pass.
None of these fares will be bettered by playing around with splitting fares, and going through a middleman. All of these can be purchased from any rail company website (in this case I have used Northern, although none of these trips use Northern, bar maybe a part of the GLA-LIV, so you don't need to use the websites of in this example between 4 and 6 different companies.

There's a lot of good advice here already.

The FAQs on the Senior Railcard site include this one:

Q: Which train companies give Railcard discounts?

A: You can use your Railcard on all franchised train operating
companies that provide services within England, Scotland and Wales.
Railcards do not give discounts on Eurostar services, Charter
services, and Heritage Railways unless state otherwise.

That FAQ has a live link to "franchised train operating companies" which takes you to a list here: https://www.railcard.co.uk/buy-train-tickets/. That page also says you can check with your "local train operating company," and you've been given the Lumo link already.

Prior answers have included information on railcard limitations on time of travel where applicable, I think.

You mentioned a BritRail pass. Having used BritRail passes, I can confirm that a BritRail pass is almost never a money-saver compared to careful shopping for train tickets online. Where it's been worth it to me, is the flexibility to change plans at the last minute - see last paragraph.

BTW, my strong preference when researching available train journeys, is to always start at https://www.nationalrail.co.uk/.

[Where the BritRail pass comes into its own, IMO, is in flexibility, especially on train trips that tend to have higher fares. I saved a lot of money by using it on a few long journeys - one was York to Penzance - when my itinerary changed after I was on the ground in the UK. With the pass, I could easily take a different train than I'd originally planned. If things had gone as first planned, the BritRail pass cost definitely exceeded what I'd likely have spent on advance fare tickets. The BritRail pass was worth it to me on the two UK trips where I've used it, but obviously YMMV, and I don't just blindly buy one. And I don't use a BritRail pass for a short trip such as London - Bletchley, or Glasgow -Edinburgh, where walk-up fares aren't expensive. There's a cost for the BritRail flexibility and convenience, which may or may not be acceptable. Because I think people may assume that a "BritRail pass" is automatically a money-saver, I think it can be helpful to point out its benefits and costs, because IMO it's not primarily a money saver - no matter how they market it, lol. ]

It looks like you'll be visiting some good places. I hope you enjoy your trip!

It's interesting that the National Rail page doesn't list Lumo as accepting Senior Railcards.
The Open Access Operators, that is the non franchised operators, like Lumo, are not legally obliged to accept railcards. However they all seem to do so, as it is in their commercial interest not to alienate those groups of people.
At start up I don't think Lumo did, so maybe the National Rail page is just out of date.

Thanks to all for the good advice. I think I'm all straightened out now. In this case there was almost too much good information floating around on the various websites, and I got off track when I saw that map on the Britrail site. I always consult Seat61 if I have a rail question, but again got bogged down with such an abundance of choices. I hope all of your patient explanations to me will be helpful to others.

@nancycantravel - I've learned a few bits here and there about UK train travel, but I can get confused and feel like I've fallen down a rabbit hole when something new to me pops up. Then I have to go back to the helpful resources, and work my way through the info again. I appreciate all the knowledge that is shared here on this forum.

Not to hijack your topic, but thanks for posting your questions and sparking this discussion. As it happens, I'm planning the details of my three week visit to the UK in May. Last night I took the plunge: bought a digital senior railcard and booked my first rail journey (King's Cross --> Edinburgh) on the LNER website. IIRC I've saved most of the cost of the railcard on that ticket. The dates of the rest of my rail journeys aren't yet live on the National Rail site or the train operators' sites. I've set up email alerts with a couple of the TOCs so I'll know when I can book those journeys.