Evicting month to month tenancy

[Judy A.]

I posted a few months back about taking over my in-laws two family home in Dorchester after the death of my father in law. Before my father in law passed he rented two rooms in his residence to people from his church. There was no lease just a verbal agreement of month to month. He told one of the tenants they needed to leave but she said she couldn’t find affordable housing so she couldn’t leave. My mother and sister in law want her out now immediately. The tenant is saying that she is on a list for affordable housing and that if we start the eviction process it will help her get the affordable housing(I don’t believe this but this is what she told my husband). My husband had her sign a notice to quit terminating tendency July 31st. We have never done anything like this before. How long will it take for us to get her out? What options do we have? Should we get a lawyer? Thanks!!!