Rail travel from either Santander or Bilbao to Lisbon

I don’t have any routes to recommend, but here’s the info:

In Spain, you can take it on Cercanias and some Regional trains without reservation.

It looks like on Avant, Media Distancia, and other Regional trains, you need a reservation for the bike. If you’re travelling with a rail pass you can’t do it online. You have to do it at the station (subject to availability). You can’t take them on other trains without disassembling.

https://www.renfe.com/es/en/travel/informacion-util/luggage/bicycles-and-kick-scooters-_non-electric_#xd_co_f=YTBjZTllMmEtNzMyMy00ZmZlLWE4M2MtYmVkZWVlMWRlZjA4~

If you are travelling with a non-disassembled bicycle:

You can travel with your bike without folding or disassembling it on all our trains without booking a seat on Cercanías (commuter), Regional and Proximity trains, free of charge and without the need for booking in advance. Look for the "Accepted bicycle without booking in advance" label when buying your ticket on the website. 
On Avant (mid-distance high-speed), Media Distancia (mid-distance), regional and Proximity trains with reserved seating, you must purchase the "Train+bike" add-on, allowing you to travel seated next to the space where you can place your bicycle, at no additional cost. Look for the "Bicycle seat available" label when buying your ticket on the website. If you have a pass, you will not be eligible for the bicycle add-on when you validate your trip, so you must go to a ticket office in your station.
On commercial services (AVE (high-speed), AVE Internacional, AVLO, Alvia, Euromed and Intercity) it is not possible to travel with bicycles that have not been disassembly, so they must be folded or disassembled.

You will probably need to cross reference that information with the timetables, and with the advice on Seat61 on routes to Portugal.

In Portugal, it looks like you can’t travel on the fastest AP trains without disassembling, but other trains seem to be OK - subject to some very specific rules on which coach to sit in, and what time of day!

You may be able to book reservations in advance via a Renfe agent. 1.5 years ago I used International Rail (mailed them at sales@internationalrail.com) for Renfe reservations and they mailed them to me. You pay in GBP and their prices were 16-17% higher than Renfe's prices in euro. There was also a GBP 10 booking fee per order, so if you use them, do all resrvations in 1 order. I don't know any other Renfe agents that accept orders via mail.