There are several ways to repair this type of condition.
The "pro" way is to buy a self-adhesive copper donut (you used to be able to get them, not sure any more), and some copper trace tape. You GENTLY scrape away the solder mask with an Xacto knife to reveal some bare copper trace. Also, cut and remove any lifted portion of the original copper trace that may exist. Put down a pad at the component hole, use the copper tape to connect the donut to the exposed trace, then flow solder across the joints at the newly exposed trace, and the donut hole. Then put in the component leg and re-solder. Afterwards, some people use a type of paint to cover over the repair.
However, most "pros" usually did field repairs by scraping away the solder mask on the trace, and cutting away the lifted portions. Then they'd use a piece of wire and/or the leg of the component, and solder this to the exposed trace (then solder that to the component leg, if you are using a separate piece of wire).
Now comes the most important part: after repairing the trace, a lot of techs would use hot glue to cover-over the repair area to guarantee that any stress on the wire / component leg does not continue to lift the existing, undamaged copper trace. Plus...it acts like a very crude solder mask.
After soldering, usually you used a little flux remover (if I recall, either alcohol or nail polish remover worked just as effectively) to get rid of any remaining rosin / flux debris before the hot glue or nail polish went down. Put some on end of a Q-tip and gently swab the area until clean.
The first method was usually done in something like a repair warehouse where the fix had to look pretty and innocuous. The latter was used to get stuff running in the field. I even think some people used fingernail polish instead of hot glue. Anything to stabilize the trace, and protect it from oxidation.
Another alternative is to use a piece of wire to bypass the defective trace entirely. It depends on what's lifted, where something is located, and what's the easiest solution. I've seen more than my fair share of board corrections (a lot of circuit boards were made with an error or two in layout, and they are fixed after-the-fact) where they just cut a trace with an Xacto, and then run a thin wire from one point on the board to the other.
In any case, you want to use something like hot glue to prevent stuff from moving, and breaking your fix. How much and where depends on the type of fix.
(And I put "pro" in quotes because different professional techs had different techniques or had to work by different guidelines to achieve the very same thing. Some of these did not look so "professional", but worked all the same.)