The screw-on type pumps don’t work too well with removable valve cores. Lezyne pumps are really bad for this, in fact they are so bad my initial thoughts were that’s what you had.
Options:
- Use a pair of pliers to tighten down the valve core that it doesn’t come undone when you remove the pump.
- Get a pump with a lever action fitting.
The problem with the first is that if you need to lend your pump to someone who has a removable valve core and they haven’t tightened things down then you’ll remove their core!