Professional lino layers use a special hot air gun and coloured (plastic) filler rod to "weld" all cuts/ joins etc. I'm sure they can do same on tears. Might be worth considering if the covering was good quality.
The other way is to trim the tear into perhaps a circle or an oval shape and insert a new piece of lino into it and glue it down well. Also try and get glue under the lino around the tear. Was there any spare lino left over when it was installed?