Hi Melissa: Some thoughts:
1) First make sure the flooring is true linoleum -- that is, thick and based on cork, linseed oil, etc -- and not one of the many competitive products of the past, like Congoleum (which was asphalt based) that sought the same market and ultimately used the Linoleum name.
2) Over many years of following the subject, I've never heard of any successful attempt to revivify crumbling linoleum (which in its true form is pretty durable stuff), though maybe someone out there has cracked this puzzle. If this is a museum type situation, suggest removing and saving what you can of the historic "linoleum" and then using new flooring that approximates the old pattern, if you can find something similar enough. Hope this helps.