If you do claim on your own daily, even hourly from the LTC faucet, you get very, very small fraction of litecoin to your coinpot wallet plus the Coinpot tokens (btw, you can claim also dash, dogecoin, bitcoin cash to your coinpot and then convert them all to LTC as it is supposed to be cheaper for withdrawal).
You can try to claim, but let me tell you how much I made by claiming for 3 months, regularly dash, dogecoin, BCH and LTC to coinpot: 0.00349831 LTC which at today rate is 0,30 $. In my opinion, claiming from faucet, is not worthed, maybe if you think longterm and really have enough time.
In case you plan and have a good referral system, then probably is better.
To mine Litecoin, is difficult...maybe try another coin and buy Litecoin separately.