When I'm working on mine I have the center stand down and attach my strap roughly over the stand. Lets me remove the wheel from either end with an additional strap or jack to ensure it stays up. Real careful with a second jack, don't want to unload the centerstand....
In general it's nice to have the weight off the tires to avoid flat spotting and keep from adding to spring sag.
My harborfright lift is old, has seen a LOT of use and may not have been the tightest when it was new, bike/lift tends to lean right, I put a strap on the left and call it good. I also do this when bike is on the side stand, a strap on left so no chance of wrenching or other leverage causing bike to flop over away from the side stand.
A story: (natch) working on front brake, bike on lift, on side stand,
no strap
.... ready to bleed, force fluid up through MC, turn bars full left angle up, when the bike starts tipping off the side stand, towards me, I get under bar and push up, instead of bike tipping back onto the side stand,
the lift rolls
away from me on it's front casters. JUST before the full ugly happens I manage to get one foot on lift and stop the side motion, achieve a fragile balance and slowly get things back to stabile Woosh. In a situation like this there's always a loop running Am I going to get hurt, crushed if this goes bad? If so I'll stand back and let the shlitz fly, motorcycle and shop stuff can be replaced. My body part rehab gets long, EXPENSIVE and extremely inconvenient.