is the lino stuck to the floor?
if not i would try this (disclaimer; i have never ever tried this so if it all goes horribly wrong you cant blame me and i think i learned this when learning how to lay turf not lino or carpet!
)
get your spare piece of lino and gently wiggle in the hole so that it lies flat (the old lino on top of the new bit) get me so far??
then with a sharp stanley knife and a steel rule, cut a square that takes the whole hole ( :roll: ), but make sure your knife cut goes right through BOTH layers of lino.
peel off all the cut layers making sure to find all the remnants that are now left under the edges of your new bigger hole.
so you should have a square with the max assisted hole in it, a frame type bit from your new piece AND....... wait for it.....
a new square that is exactly the same size and shape as the hole in your floor, even if you didnt get the angles of your square correct!! bung that in the hole to check it does in fact fit, and then stick the whole lot down including the edges of your hole.
it works for repairing a lawn, your on your own if you decide to give it a go on your kitchen floor though :lol: :lol: :lol:
if the lino is stuck to the floor all over, i recommend a funky new mat from ikea to hide it with