I have done research on landlords breaking leases, but I am realizing that my "lease" is actually a "roommate agreement" that the landlord (who also lives in the house with my partner and I) wrote up and we all signed upon move-in. I think it is still legally just like a lease, but the issue is:
Our lease term is six months and states simply "roommates who move out while this agreement is in effect (6 months lease then month to month) continue to have financial responsibility unless the owner releases them from this responsibility in writing"
She has told us after only one and a half months that we need move out. She has given us no reason, and there have been no problems (we have been good roommates and take care of her three dogs while she is out of town, which is all the time).
Is she in violation of landlord breaking a lease, even though it is technically called a roommate agreement?
Can we hold her accountable financially for the rest of the six months if we cannot find a comparable price for housing? I have read that the landlord can be responsible for the difference in cost when they break a lease term.
Thanks for your advice...

Yes you have a lease. A lease is any contract that provides use (but not ownership) of something for a period. You were provided use of the premises for 6 months.

That agreement is binding and cannot be broken without cause or the agreement of both parties.

If she wants you to move out early, let her buy you out of the lease. Otherwise you can stay until the 6 months is up.