I don't know how long you're planning on living in your present house - but if you have anything tested for hazardous substances such as aesbestos, you'll have to disclose it when you sell unless you completely remove it (at considerable expense.) You may even be FORCED to remove it - depending on local regulations.
My advice(s) is(are): - lay a new floor over the old floor and seal it in there forever. - you can maybe lift off the old tile with minimal exposure to danger - depends on how well it's stuck to the floor. Wear a mask and keep the dust to a minimum.
Whatever you do, don't sand it unless you've had it tested and found that it's asbestos-free for sure.
...But getting it tested may be asking for trouble. Sometimes it's best not to know. (And proceed with caution under the assumption that there probably is asbestos.)
You didn't say how old the linoleum was ... You might check with someone more knowledgable on the subject - but real linoleum laid in the 30s probably doesn't have asbestos in it. I thought I heard that the glue used to lay down linoleum in the 70s was the more common hazard. Call your local EPA and ask them.