Lloyds is one of the four clearing banks through which all UK banks must work. Last month it ordered the Islamic Bank of Britain to freeze Palestinian aid charity Interpal's account for an indefinite period, without any explanation.
The MPs say Lloyds' decision could set a precedent for banks to target other charities. Four MPs signed the motion, started by Labour MP Jeremy Corbyn last week.
Two years ago, the Charity Commission began an investigation into alleged links between the charity and Palestinian Islamist group Hamas. Previous investigations by the commission found there was no evidence to support the allegations.
A spokeswoman for Lloyds declined to comment.