I made a disparaging remark about my PB mini pump yesterday. I figured out how to fix it last night for those interested, although having dissembled it and seeing how it is put together, I still plan on taking a Lezyne on tour this spring.
If you cant get the pump head over the schrader valve enough to get air in the tube cut 1/8 inch off of the rubber tube piece that is directly under the screw-on cap on the pump head. This brings the little nub at the bottom closer to the top of the schrader valve body. You may find that you dont need to do this with some tubes and with others it is a necessity.