yes it is easily patched. A repair piece can be removed from under an appliance and once the hole is carefully cut out and the plug even more carefully cut to fit.. You will barely notice it is there. I said Barely.....
Generally, flooring installers cut to a pattern line and they use a special type of glue (available from a flooring contractor or supply house). The patch is cut larger than your hole (cut to the pattern line), then the "cut out piece" is laid upon the new piece (same pattern) and cut EXACTLY the same. Then it is glued down and the seam glue put at the seams, then covered with a very heavy weight (such as a piece of railroad track). When finished, you shouldn't notice any patch at all...unless you use a magnifying glass. THIS is probably a job that you should have a professional flooring guy do for you. I have done it, but it truly is a chore to do it right.
If the flooring is very old it's probably faded so a piece from under an appliance might be a different shade now. Check it before you do any cutting.
It's not hard to do. If there's no fading, just cut a piece from a hidden spot that is larger than the hole, and don't cut it in a straight square, a odd shaped cut is easy to place and doesn't show up as much. I like to make oval cuts. Tape it over the hole, matching the pattern, then cut thru both layers. That will make the patch piece fit exactly. Then get a good glue and glue the patch in place. Put something heavy over it and don't move it for the length of time it takes the glue to dry. I'd leave it extra time just to be sure.
When your done, give the entire floor a good waxing. You probably will never be able to tell where the patch was placed.
Since it's a little bitty hole, I wonder if you could use some of that stuff in a tube that's made for repairing leather furniture. It's made to be used with heat that might be to hot for the linoleum, but it might be worth a try. I'd try it on a spot that isn't visible and if it works, then go for it.
Depending on what color the lino is, you can get silicone sealant for tub areas that frequently blend quite nicely and if you can't get a nice match, I was told you can enhance the colors with model paint.
==>once the hole is carefully cut out and the plug even more carefully cut to fit..
The easier way is to lay a small piece over top of the hole -- mabe 10% bigger than the hole. Lay the patch piece directly over top of the hole, and then cut it, cutting through *both* the new patch and the old floor. Now, you've got an identical patch with an identical hole, both made with the exact same cuts. You'll be cutting through two layers (the old and the new patch) so you'll need to make sure your blade is sharp.
I know that chocolate chips won't do it! When my uncle was young (right after WWII) he lit his can of homemade gunpowder on fire in grandma's kitchen and tried to cover it up with chocolate chips, but she saw it as soon as she walked in. He was in TROUBLE!!
Tom helps a pair of Sacramento homeowners repair a damaged section of vinyl flooring in their kitchen using a remnant left over from the original installation. Tom explains that the floor's "pattern" repeats itself every few feet, so he begins by laying the remnant over the damaged area, being careful to match the pattern with the surrounding floor. He tapes the remnant on top of the existing floor and cuts out the patch along the simulated grout lines. This allows him to cut both the new piece and old piece at the same time [with a NEW utility knife blade held at right angle to the floor] , ensuring a perfect fit. Tom uses the straight side of a notched trowel as a straightedge to guide the utility knife's blade along the grout lines. He then uses a wide-blade knife to pry up the old piece of flooring and scrape away the old adhesive. He then uses the notched trowel to apply new adhesive. Tom inserts the new patch and rolls it flat using a special flooring roller, being careful to wipe up all of the glue that has squeezed out of the seam. Finally, Tom seals the seams of the patch with a special seam-sealer which will keep water out when cleaning the floor.