You may not ever want to write your own psalm, but if you do, here’s advice on how to do it.
You don’t have to restrict yourself to a psalm of lament, though. There are 5 kind of psalms: praise, wisdom, royal, thanksgiving, lament, according to this. Feel free to write the one you see fit.
P.S. I got interested in this after finding out Churchill wrote his speeches in psalm style. You can read more about that, here. Or see an example of it below.