it's a good question and an interesting problem.

you will always need computers to sign, send and verify transactions. but these operations are lightweight such that you don't need much power. all of the above can be accomplished via something as simple as a raspberry pi connected to a solar array.

the real challenge IMO is robust, censorship resistant bandwidth. bootstrapping a node requires downloading and verifying the entire ~500gb chain. you can trust someone else's node, but this may not be wise in an adversarial environment (and in bitcoin land we do like our "worst case scenario" thought experiments). it's even trickier when talking about lightning as nodes must be online to receive payments.