Slide a piece of alumiunm sheetmetal (stepflashing works great) with some adhesive on the back side of patch slide thru the linoleum tear. Take a littie adhesvive apply it to the back side of linoleum tear, press it firmly apply weight to the repair area. let dry/cure. Take some white-out and fill the tear seam, let dry.
Of Course if the linoleum isn't white find a suitable silcone colored caulk for seam filling, you need to let the silcone cure for 24 hrs. I like white-out due to the fact that it's very controllable during application, try using a cute tee if your using silcone.
Make sure the aluiumn has a 1 inch or bigger overlay than the hole; trim any sharp edges and round the corners .
