The best and most effective way to get up lenolium adhesive and all is Methylene Chloride. It is nasty stuff the safety equipment "Required" to even handle the container is so expensive you'd rather pay someone else to do what you're talking about.
There are adhesive removers they will only make part of the job easier the glue will come off the floor but then you have a mess of wet and now very sticky smelly stuff you have to also clean from your floor before you can use it again.
The easy part removing the top the vinyl itself will pull right off the backing and the backing and adhesive remain on the floor. It is possible to put another floor on top of that but I wouldn't recomend it. If your lenolium while old and worn is not coming up off the floor at all in the edges and corners, just leave it there you're not gonna see it again when it's covered and it does act as a vapor barrier.
another thing you want to know before you dump chemicals on it is do you have new or old style old style was made with asbestos. to check for yourself tear off a piece of the top vinyl and look at the bottom of that piece white specs stuck to it indicate it may be asbestos. bend it and smell it if you smell a slightly sweet smell that is Lin seed Oil and that is the newer style and you don't need to worry so much about it both can be removed easily from the floor and no matter what methods used it takes time and patience.
I'm actually working on my kitchen right now and just using my flexible long handled scrapper it's about 12" wide and if you dig the corner into the paper you can start it to peel and a few good shoves and about a 12 inch square is coming loose glue and all. No solvents etc just elbow grease and determination. Just don't rush yourself and be cautious of chemicals. Your area you live and the floor you are working with greatly matter in what you use to do the job check with your local hazardouse waiste disposal place and ask someone who does this for a living what they recomend.
should I find a chemical that works well I'll let you know but for me I have two small ones and two dogs I'd rather not poison my house.
-Andy the cable guy
I love to work on my house would love to help you with yours!