OP Updated.
Bitlum wallet is an alternative that can also be used to make LN transactions. Based on other people is experiences, Bitlum wallets charge 1 satoshi per transaction.
Never heard about Bitlum wallet. You can try with eclair wallet for Android which I am doing at the moment. By the way, no wallet charge fee for any transaction. Bitlum is a wallet which might support LN but this has no connection with charging 1 satoshi per transaction. As like BitCryptex said above, the fee will be charged by the route and it can be different depending on which Route you are using.