Am I liable if a lamp I repair for a friend catches fire and causes damage?

If I repair a desk lamp for a friend and it catches fire and causes damage, am I liable? Would it be better for me to not accept compensation for repair so as not to enter into an implied contract and thus assuming liability?

As usual, 'it depends.' Are you charging the friend for the work? Is the friend the suing type?
In general I think it's safe to say no, you aren't liable, when you have a friendly arrangement with no contract.
A friendly arrangement with no written contract but MONEY changing hands casts a cloud over this a bit. But heck, I've fixed countless lamps of my own over 67 years and never had one burn up or cause damage.
If you are unsure of your abilities or the friend's tendency to sue, don't do it.
The friend can't easily prove that the lamp wasn't going to cause damage anyway, or that you promised that it wouldn't (unless you do), and unless the damage is extensive and clearly caused by the lamp, it's not even worth the legal costs to sue you.

For pity's sake, how much were you planning to charge? Have him buy you some food, take you to dinner, do some dog sitting, get your car's oil changed....

This is time honored barter. Of course the IRS wants you to pay taxes on barter. Does ANYONE DO THAT??? No, not unless it's a mansion bartered for a yacht, and not even then, I'll bet.

Friends are friends and we generally do stuff for free, unless it's part of our daily livelihood.

How bad are you at repairing lamps that you're worried it will catch fire? Maybe you're not the right person for this job if this is a concern.

If you are not an experienced electrician and if you were negligent in doing the repair, then yes you could be held liable if the friend sues. However negligence may be hard to prove.