So, I've unlocked It Lives! before getting all the endings for beating Mom's Heart. Is there any way to unlock them now, or is it no longer possible?
As far as I know, after killing Mom's heart 11 times it will be permanently replaced by It Lives. So if you've unlocked It Lives! you should already have the first 11 endings.
Endings 1 - 11 are available after defeating Mom's Heart. Each time you defeat the boss a new ending is unlocked.
But if you mean that you still miss Mom's Heart related achievements, you can unlock them also beating It Lives!, as you can see here It Lives! has the same bunch of achievements for Mom's Heart.
No. It Lives does not lock you out of anything that you would get from Mom's Heart, as It Lives is just a more difficult version of Mom's Heart. Defeating It Lives will count for all unlocks that are contingent on beating Mom's Heart.
It is a stronger version of Mom's Heart that summons bosses alongside regular Womb/Utero enemies.
Lower on the page, it lists all of the Mom's Heart-related unlocks as related unlocks for It Lives, as well.
If you are referring to the endings, as @Pinckerman stated, you should have unlocked the Mom's Heart-related endings before unlocking It Lives. It is not possible to miss any of those endings while still unlocking It Lives.