The biggest gun in the arsenal when it comes to removing stains from linoleum is a process called "procking". Or, at least, that's what I've been told it's called.
Apply some bleach to your linoleum with a Q-tip in an inconspicuous area. If the bleach doesn't take any colour out of the linoleum, you're OK to proceed with the procking.
Take a white cotton rag (old torn up bed linens are good) and get it saturated with bleach so that it's almost dripping. Don't use a coloured rag because the dye from the rag could end up leaving ANOTHER stain on your linoleum. Set that over the stain and cover the rag with something so that the bleach doesn't dry out. If it's not too large of a stain, a large porcelain bowl will do provided it makes a good seal around the perimeter of the bowl. Otherwise, use a clear plastic bag to cover the bleach soaked rag and weigh the perimeter of the plastic bag down with something. (They sell large clear plastic garbage bags for people to put compostable materials in like grass clippings and leaves, so any place that sells composting supplies will probably sell large clear plastic bags to0. I use a small link steel chain to weigh down the plastic around it's perimeter, but straight sticks will work well too.
Leave that bleach on the stain for a half hour and see if it seems to be doing any good. If so, leave it on over night. Check occasionally to ensure the bleach isn't taking the colour out of your linoleum. If it doesn't within the first hour, it shouldn't.