Traveling to Lake District from Seattle

Look into flights to Manchester, especially if you want to take the train.

Try google flights with your dates.

You're asking fairly subjective questions on Premium Economy, and I think you mean
to be specific to your travel plans even though you don't state what they are.

A little more detail on your initial ideas would help people give you better information.

You also need to be certain of the terms you use. "Premium Economy" is the standard
term for the class of service between economy and business these days. Different
airlines may give this class their own name, but it can also easily be confused with things
like Economy Plus on United, which is just a bit more legroom. If you have seen the
terms "Economy Comfort" or "Premium Comfort" used for a specific airline, a bit more
info would be helpful.

Finally, if you are looking for ratings, you can get those from a web search yourself. If
you are looking for input from others on the forum, it will be more opinions and based on
personal experience (and preference), and you should ask about specifics of the class
that matter to you (food, leg room, seat width, baggage allowance, amenity kit, etc.).

This vacation (from a separate DM) is actually commencing in Scotland then continuing to the Lake District.

Thus the suggestion would be to research airlines flying in to Glasgow/Edinburgh/Inverness. From SeaTac to the best of my knowledge that means connecting (on the same ticket) at LHR, Dublin, Iceland (Keflavik), Paris CDG or Amsterdam Schiphol.
I am discounting Aberdeen given the OP's proposed itinerary within Scotland.

Or connecting for a Scottish airport domestically in the United States.

It would be possible to open jaw at the end of the trip back through Manchester to the US, but as a local resident it is as easy and fast to go to Edinburgh/Glasgow airports from the Lake District as it is to Manchester.

Given the ease of the journey back from the Lake District to Heathrow it is almost as easy to go to LHR for the return direct flight as opposed to going to any other airport, going through airport rigmarole, and allowing enough connection time between flights. Normally about 4 hours from Penrith to Watford Junction then the Rail Air Bus if you want to avoid the tube or other rail journey through London. It seems counter intuitive but the fastest rail connection from Penrith to Watford Junction is often a same ticket connection through Euston.
In my own planning I see very little practical benefit (from the Lake District) of flying to SeaTac other than from Heathrow. Even connecting out of Manchester (in theory the better alternative) doesn't actually confer any obvious time benefit that I have ever traced. I would be travelling in Standard Economy, so whether travelling in a higher class alters that equation subtly I don't know.