Floor pump blowing wet air?
Yes, floor pumps can condense water in them. The water is from atmospheric water vapor. When the pump walls are colder than the surrounding air, the vapor can condense just like dew forms on leaves in the morning. Temperature swings assist in the formation of dew and this is made worse by leaving it on concrete, which is not only often much colder than the surrounding air, but also retains moisture.

After a while, the moisture in the pump will build up to the point where it has to get blown out the next time you use it. Especially, pumps like the Lezyne (which I also have) which are single-action designs, the top of the pump is open to atmospheric air and so the moisture can easily condense on the inner walls above the piston and trickle down into the main chamber.

How to get rid of it: 

1) Easy way: Dry pump a few times (i.e., pump it a few times with nothing attached) until nothing comes out. If you can do this outside in the sun, even better.

2) Slightly harder way: Do #1 first, then disassemble the top of the pump so that it's open to air. Take the piston out. Let everything air dry or dry on top of a radiator. While you have it apart, grease the piston seal slightly with the vendor approved lubricant -- usually any light silicon grease that is safe for teflon/rubber/leather.

How to prevent it from happening

Don't store your pump in a basement or garage where there is cool/damp air. Keep the pump off concrete. Store it somewhere where there is cool/dry air (best) or warm/dry air (second best). 

If that's not an option, you could also hang the pump upside down (with the handle in the stored configuration) so that any condensate that forms in the piston or on the handle will drip down. Keeping it away from the concrete floor would be an added bonus.

Bonus

Finally, here's a youtube video made by Lezyne showing how to overhaul their pump: