I assume because there are pulmonary issues the cath referenced is a right heart catheterization to measure the pressure in the main pulmonary arteries and that is an invasive pulmonary test. Elevated pressure could indicate a clot in the pulmonary vessel and/or pulmonary emboli.
There is PFT called a spirometer. This noninvasive test measures how much air your lungs can hold, and the airflow in and out of your lungs. During the test, you'll blow into a simple instrument called a spirometer. This is usually the first and most commonly done lung function test, and measures how much and how quickly one can move air out of your lungs. For the procedure, one breathes into a mouthpiece attached to a recording device (spirometer). The information collected by the spirometer may be printed out on a chart called a spirogram
Following a cath and providing time to determine the outcome of the procedure, and following the recommended prep would determine the time between the two tests would be appropriate. Your question asks how soon "should" a pulmonary test be performed after a cath? A PFT is not always necessary and depends on the diagnosic objective.
Thanks for sharng and your question. Take care,
Ken