We strongly recommend that you remove the old layer of vinyl floor covering prior to installing new - unless the existing linoleum is firmly attached to the floor below it and the surface is absolutely smooth and without pattern impression.
Actually, linoleum is not terribly difficult to remove. The trick is heat. Heat can be applied with a hot air blower, a household iron using a towel as an insulator (preventing lino melt down), or if you're handy with tools, a blow torch with a flame-spreading nozzle. Heat helps removal by softening the glue to a gummy-yet-workable state.
An overzealous do-it-yourselfer may assume that attempting removal without heat would be a time saver. Nothing could be less correct. Without heat, the top layer usually is pulled away from the backing and the job becomes twice as difficult. Don't forget to razor knife through any difficult parts.