Hi.

TLDR: If you augment a card it keeps its Ability Level (A.lv). Going from 2* to 3* drops the 'Lesser' but keeps the A.Lv, so use any fodder you have before augmenting to 3*. If you're want to use this higher A.Lv card for building up another card's A.Lv, save it for higher A.lvs when A.Lv upgrading becomes harder.

Longer explanation

If you raise the ability level of a 2* 'Lesser', when you augment it to 3*, it drops the 'lesser but keeps the A.Lvs. So before augmenting any monster card to 3*, be sure to use up any 2* fodder you might already have (but don't hold off the augment just to farm more 2*s). The highest you can level a 2* is A.Lv 4.

If you do end up with a higher level 3*, and want to use it to help max out a drawn card with the same ability, don't use it right away! Rather farm the 3* cards that monsters will now drop, and use those at first. The higher the A.Lv of the card you're building, the lower the success rate gained from each ingredient card you use. However increasing the A.Lv of the ingredient card increases the success rate gain. So you'd rather re-farm A.Lv1 cards for the first 3 A.Lvs when it's cheap and easy, and only use that higher level first card to help later, on the higher A.Lvs.