Can you use the same seed for normal BTC and Lightning wallets? If I generated 24 words from a Ledger Nano, can I import these to a lightning network wallet e.g. Eclair?
A lightning network wallet can be compatible with a Ledger Nano generated wallet, but doesn't have to be.

Ledger nano generates seeds (the 24 words) using BIP 32/BIP 39/BIP 44. 

I checked to see what format eclair uses, and it seems to use BIP 49 instead of BIP 44. This seems to suggest that the seeds are incompatible, but I haven't confirmed this.

If you want to do so, you can try importing your Ledger seeds into eclair, which is a non-descructive action (i.e. it won't affect your wallet/funds).