Most of the time, the sqeaking comes from the leather flexing against the ends of the frame on each side. You can eliminate this by: 1) cutting a 3/4" square from an old innertube, then: 2) hold the skirts away from the frame ends: 3) insert the rubber squares as far into the space between the leather and frame as possible.

It helps to have an assistant pull the skirts apart, while you use a needle-nose plier to slip the square up into the gap.

Rarely is it the seatpost that sqeaks. Sometimes it may be the adjustment screw up front, but usually it's the frame/leather. TEST: Before going with the above suggestion, just use your hands and gently squeeze the skirts together slightly as you carefully listen to pin-point the sqeak. You should be able to quickly locate it at the widest part of the saddle, at the frame ends.

Lifting the bike by the back of the saddle will do no harm - the frame is there and makes an excellent hand hold.