I believe it's always a good idea to get the weight off the tires when being stored for extended periods. If nothing else, use a plank to drive on to get off the concrete. Wood would insolate from the damp concrete. I would however be a little nervous leaving the bike on the lift. I use my lift to raise the bike up & chock the frame with some 4X4s. Lower the lift just a tad. This way you are 1) not dependent on the lift to hold the bike up. 2) using the lift as a secondary should the 4X4s slip, and 3) a good place to store the lift out of the way.
Thank goodness for catalogs and spring rallies. Without the drool and dreams, not sure I'd make it through the winter.
I may sound a little too cautious, but here goes . . .
I store my bike on a lift but take some precautions against the possibility of failure of either the bottle jack or some other part of the lift.
1. Of course, I use the built-in "stops" on the jack and release pressure on the bottle jack by lowering the lift to one of the stops.
2. I put some lumber under the tires so that each tire is barely above the wood. With the bike strapped to the jack, if there should be some failure of the jack, the straps should keep the bike upright and the wood should keep it from falling to the floor.
3. I detach the bottle jack from the lift, lower the bottle jack piston, and place a block of wood between the lift and the top of the piston. This may not be necessary but I decided that I would rather have the bottle jack in a "bottomed out" position for the next few months rather than in an extended position.
I hope this doesn't sound like I have gone from being merely "cautious" to being PARANOID!