Simply put, Lightning Network nodes constantly signs new commitment transactions, which record the current balance of the channel, whenever a channel is updated. Both parties exchange revocation keys for the latest commitment transaction while signing a new one. It's technically impossible to derive your partner's revocation keys and any past commitment transactions from your mnemonic phrase.

LND backup file lets you reconnect to your peers and ask them to close your channel. Note that you won't be able to verify if the other party published the latest commitment transaction. You won't be able to broadcast a penalty transaction to defend yourself. Also, if the other party is offline or refuses your request (despite signalling data-loss protection), you won't be able to recover your funds.

c-lightning has a backup plugin which maintains a full channel database backup to a remote directory. You won't have to close any of your channels if you restore it.