Can we be inactive if our referals are active?

Yup! Even if you aren't active, if your referrals are active you will still earn money! I've taken breaks from MyLot that lasted for several months, and during that time many of my referrals were still active. And when I came back to MyLot, sure enough- my referral earnings had still been accumulating even though I wasn't earning anything at all for my participation since I wasn't active.