The tire is inflated, but unscrewing the pump head brings the valve core out with it and releases the air. One possible cause is a loose core. Lezyne describes this even with new inner tubes; an overtightened pump head can make the problem worse.
First establish whether that particular Presta valve has a removable core. Not all do. A valve-core tool engages the flat sides of a removable core for installation. This is a separate operation from opening the little nut at the valve tip before pumping.
With Lezyne ABS Flip Chuck and ABS-1 Pro heads, the core should be secured more firmly than the pump head. Thread the head on only far enough to make an airtight seal, without forcing it against its stop. A sound seal matters more than maximum tightening force.
After inflation, these heads’ ABS button releases pressure from the pump and hose when used with Presta, easing removal. With Schrader, it can release air from the tire too. Follow the instructions for your own pump: similar-looking buttons and heads do not necessarily work alike.