Train ticket prices/Southern Railway

The answer is that you are looking too soon for train fares. Like with many operators they are currently only in until the summer timetable change on 21 May.
Looking for a closer date, after 0954 in the morning, you will find VIC to Lewes for £9.50 (even just 2 days from now it is £15.50).
It's the same for Lewes to Gatwick - book ahead and you will get that (after 0955) for £9.50.
You will likely need to wait for several weeks yet for these fares to appear- but the evidence and experience is that there is no rush- as close as 3 or 4 weeks beforehand will do.
I'm not quite clear whether your Nat Ex question is about from Lewes to LHR, or Vic to LHR, but Nat Ex have heavily reduced their routes since Covid and are not currently running from Lewes, so I think you mean Vic.
Gatwick to Heathrow

Please forgive me if I am being dense with your Nat Ex questions. LGW to LHR- fares vary between £17.80 and £27, very frequent service day and night, no advantage to pre-booking, no return fares.

Vic to LHR- there are coaches at 2359, 0215, 0240, 0330, 0400, 0500, 0700 and then every 30 minutes throughout the day for a broadly 50 minute journey. Advance fares are either £6 or £8.40. Most people would go by tube/Elizabeth line but if coach suits you, then why not.
So the web page must have been malfunctioning for you.

PS- from LHR to Vic it's much the same- coaches at 0100, 0345 then at least half hourly until midnight for £6.
If, like me, you have a coachcard (for being ancient!) then the £6 fare becomes £3.90- which is the cheapest way from LHR to London.

In the morning peak you can save £2 or so by using your Oyster to East Croydon (£6 peak, £4 off peak), changing trains and swiping out, then EC to Lewes for £26.60- a little know money saving ploy from Victoria to Gatwick as well.

To get to Heathrow by 1pm from Lewes I have just looked again, and on Wednesday 3 May and each day thereafter, the first £9.50 train to Victoria is the 0925, arriving 1036, more than enough time to reach LHR by 1pm, but even the 0821 train, arr 0936 is only £15.50, and the 0855 £13.50.
So unless you want to do Gatwick, then coach to LHR (fair enough if you do) you don't need to, and the via London route is likely faster, or at least no slower.
That far out I can see off peak singles Victoria to Lewes for as little as £6 on each and every train.
Round trip Vic to Lewes would be an Off Peak Return (valid 1 month) at £42.80, anytime return (valid 1 month) is £71.60- that is more than 2 x peak singles (!!)- another fare quirk.
So a railcard and coachcard holder, like me, could go from Lewes to Heathrow for under £8. That has to be a bargain.

Thank you SO much for your help! That certainly is a relief. If I ever knew that about booking too early, I have forgotten.

I knew something must have been wrong as it only cost £8.50 one way in 2019. It's good to know I have more than one option.

Edit: a friend of mine in London said another option is get a train from Gatwick to Farringdon and then get the Elizabeth line to Heathrow T4.

It is, except the advance fares are Southern railway route specific so you would need to buy a £9.50 etc advance fare to East Croydon, exit through the ticket gates, then go straight back in on an oyster or contactless card- that would cost £14.10 off peak, or £14.90 peak EC to Heathrow via Farringdon Elizabeth Line.
If you have gone through to Victoria on the cheap fare the tube route would be Circle or District to Hammersmith or Earls Court/change to Picc line- which is £5.60 anytime on Oyster and Contactless.
The time difference is minimal- in fact TfL journey planner reckons, surprisingly, that tube via Victoria is the faster.

It's absolutely down to personal preference.

Me, my preferences, I'd stay on the train to Victoria, then tube. But that is me. There isn't a right or wrong. There are other routes as well from East Croydon but they are not for someone with luggage unfamiliar with the area.

PS- I knew the time difference between the two routes was tight, hence why I checked TfL, but was surprised that the tube won, and that I had to force the system to give me Elizabeth line. Forgetting the fare difference, like your friend I would have thought Elizabeth Line was the narrow winner.

I certainly don't want to get lost! :) I still have time to think this over, so I will do that. Thanks again for all your help!

Sandra,

The Advance fares are now loaded into the system for the whole of June so you can now purchase any time you are ready to do so.

Thank you very much for the update. Guess I'll go ahead with that! :)