Electrical outlets show good but not working
You have a high resistance connection somewhere in the line.  I would bet that if you have the lamp plugged into one of the outlets and turned on, if you then check another outlet, it will show a low voltage. The reason the tester and meter alone don’t show a problem is that they draw very little current.

First thing to check, with the lamp on, is voltage between neutral and ground. If it’s high, the bad connection is the neutral. If hot-neutral and neutral-ground are both low voltage, the bad connection is in the hot line.

Since you say the breaker panel was recently changed out, I’d start there. If you’re comfortable working on the panel with the cover off, check for a loose wire to the breaker or neutral bus. Remove the wires, clean or cut and restrip the wires and retighten. If you’re not comfortable, call an electrician.

One more note: you didn’t give the age of the house but if it was built in the ‘60s or ‘70s, you may have aluminum wiring. If the wires look silver colored instead of copper, stop and call an electrician. Aluminum wiring needs proper treatment to avoid future overheating and house fires. Judging from your question, I doubt you’re qualified to handle aluminum.