Isn't lightening a form of proof of stake?
No. Not even close

Lightning is an off-chain transaction method. The only thing both have in common is that LN, on its own, doesn't require much additional electricity use. But LN needs a blockchain to work, and in the case of Bitcoin, a proof-of-work blockchain.
Isn't PoS completely insecure due to the nothing at stake problem?
Or is there any solution to this problem?
That's what was discussed here in the earlier postings. There are disagreeing views: Myself I think there are "solutions", or that the vulnerability is merely theoretical (in my opinion, above all, the "
bribing attacker" scenario and also "multi-chain forging" is based on unrealistic conditions). There are others that think that the "bribing attacker" are fatal to PoS systems, or that special conditions (e.g. an "oligarchy" of cooperating whales) are needed for PoS systems to work.