As to the stability, anchored or not, it depends on the lift. I have a friend with a Direct Lift PP9 Plus ((9,000 lb model) and he did not fasten it to the floor. BUT the installation manual says that anchoring to the floor is optional. This model also has a caster option so you can move it around. What does your installation manual call for?

"We live in a time when intelligent people are being silenced so that stupid people won't be offended".