I cannot advise on LN since I didn't test it out yet, but I can tell that right now the mempool is empty, hence if you want to do "small transactions", the fee should be minimal (1 sat/vByte) if you use a stand alone wallet (Bitcoin core, Electrum, and some others).
If you spend on-chain (normally) I can advise, where possible, to use SegWit (send from bc1* to bc1* addresses) and group transactions (send to multiple recipients in one transaction).
It could also be a good idea to consolidate the funds you have if you know that you have many small inputs, this should help lower the fees for future transactions.