Will a Litecoin LTC transaction with a low fee of .001 confirm? Will a low fee of less than .001 ltc confirm using the coinomi wallet? And if it doesn't how long do you have to wait for it to return the coins back to you?
I have seen transactions with 0.000224 fee are also getting confirmed.

So we can say 0.001 LTC fee is too good.

You can check current fee here 

https://bitinfocharts.com/comparison/litecoin-median_transaction_fee.html#3m