Trump can't possibly win on the legal merits here. All precedent is on the side of the House. His lawsuit is a delay tactic. Thankfully Judge Mehta has fast-tracked the case. But Trump's lawyers will eat up more time with appeals. His lawyers are just making transparently bad legal arguments to justify litigation which is solely for the purpose of delay.
By testing limits, Trump has yet again exposed another crack in our system. There ought to be a statutory fast track all the way through to the SCOTUS for litigation between branches of government involving issues of separation of powers. In CA, we do this for death penalty cases, where the appeal automatically goes to our Supreme Court, skipping the intermediate appellate courts.
Add that to the list of things we need to fix once the dems are back in power. Fortunately the repugs may not oppose it because there will be a dem in the oval and they never seem to think past a law's political impact on the party currently in power.