This is normally stipulated in a lease under forms of acceptable payment. 

You say the market’s hot, what about considering:1 taking the bank’s option to Convert to a 30 year fixed term, with maybe piti of $500/ monthly (See if they will lend you 75% of the appraised value OR use the purchase price Plus a detailed list of your costs and repairs) , and then2 selling on contract or lease option at full market price+, ie $119,000 possibly on terms.Look for 10% or more down and finance them as long as your loan is for.This would recoup your initial investment, $12,000+ and costs plus profits And give you passive income of what $200-250+ net monthly?

We spent about 5k scrubbing it up and now we have a leased signed for $775 a month.

Your best options for low or zero down is to find a property using seller financing, lease option, or get a private lender.

If you can get your best price from an owner occupant then a month to month lease would be best so you can deliver the house empty to the next buyer.If the house is really a good rental and the lease is favorable then offering it to sale to an investor with an annual lease in place with a good tenant might be best.

Looking for a lawyer in the Spring, TX/The Woodlands area, who has a background in lease issues with single family homes.

It may be easier to act like a bank offering some people a financier with a lease option  and make them your typical lease people because they  want they want home ownership someday and become an owner but they did not previously qualify for with a loan from the Bank. 

terminate lease?

Be sure to go over your paperwork and follow the rules in the lease.

If it's leased, there will likely be a lien on the home.