It's taking place off Jackwood and Endicott.
The church and its school say they've been very grateful to get parking space for free. They're not opposed to paying for it but they say the new owners are asking for too much.
It's a parking lot that's as crucial to the St. Thomas Episcopal School as any classroom or library.
"Anytime there is a school function, party, I use the parking lot," one mother told us.
But the school has never owned the parking lot. For decades, various owners of Meyerland Plaza shopping center have allowed the school to use the parking lot for free. But Meyerland Plaza, including its parking lot, were sold last fall, and the new owners want rent.
"The first number was a bit high, so we've engaged with them, talked with them; hopefully we can come to a solution," said David Browder, the rector of the church and school.
Browder's staff is working with the lot's new owner, Fidelity Realty Partners. But it's initial rent proposal of $380,000 a year was just too much for the school.
"No, no we can't do that. We just can't do that," he said.
Fidelity didn't want to talk on camera, but they told us that it is trying to work out an appropriate deal with the school. At this point, neither side seems certain what a fair price would be.
Parents say they just hope something is worked out, so they won't have to park elsewhere.
"I think the traffic will be terrible and the kids may not be as safe if I let them park here and cross the cross walk," another mother told Eyewitness News.
Both parties are hoping to reach an agreement by the start of the new school year.