Eww. That's nasty.

1- Yes. Use any silicone based Pool / Spa lubricant. If the gasket is cracked or dry, just replace it (but lube even a new one.) Apply it by squirting a liberal amount (unshelled walnut or pecan sized glob) into your GLOVED HAND. Run the o-ring through the lube so that it is ENTIRELY coated. DO NOT get the stuff on your hands or clothing. While it won't cause any harm, it's nearly IMPOSSIBLE to wash off. It is waterproof, after all. Don't even TRY to get your hand wet if you get it on there. Just wipe as much as you can off with a shop rag or paper towel.
2- When I reassemble mine, I use a healthy amount of lubricant on the o-ring and just use about 40 to 50 pounds of my body weight to seat the lid back down. You shouldn't rely on re-attaching the girdle band to bring them back together...