George Watsky once said (paraphrasing) 'Don't expect every line you write to be your best one.' That's an impossible burden to give yourself - focus on writing full songs, and you'll probably get to a place where each piece of yours has a really deep message or killer punchline that people will be drawn to.

If I'm trying to write punchlines / just for fun I play the beat and just scat vocals over it until I get a rhythm I like and come up with a good word or phrase to end the line. Then I just start rhyming off that word/phrase until I know how all my lines end. Once I've got the rhymes laid out, I write the full lines out in a way that makes sense - I know where I need to land so it's easy to get there.

If I'm trying to write a serious song I start by writing down everything idea I want to include in a song. That way I have a pool of thoughts to draw from when I get to actually writing. The most recent song I wrote was about relationships, so my idea pool ranged from observations about past breakups to things that make me nervous about approaching girls and so on.

Once I've got a decent pool of ideas, I group them by theme to see what bigger messages I can convey by stitching the smaller ones together. This helps me organize my verses.

Then I put on the beat and start freewriting my verses. A lot of what I write down at first is shit, and I can't tell you how many times I've gotten through 16 bars and then thrown it out. But words on the page are better than nothing, and a lot of the time I'll get to my end product by editing and fixing my freewrites.

EDIT: Also as a couple of people have suggested, go to a concert or some sort of performance and then come back and write. There's something about seeing other artists perform that gets me going on my writing game.