I rented a house with my boyfriend together and the landlord told me that my son and I had to leave because my ex boy friend now told him i was the problem. Can I sue him for making me move out?

Instead of suing, you need to look at your lease. If you are on the lease, see what's in place for this type of situation. If your name is not on the lease, then yes, the landlord can kick you out. If this guy is your ex-boyfriend, you don't need to be around him and neither does your child, especially if he's making allegations against you. You don't need that type of negativity.  So check out the lease and see what your options are. If this were me, I would have already been packed and gone, but that's just me.