I have never measured it, but one of the things that a florescent light does when it turns on is the initial arc, or startup method or glowing filiments at the ends of the arc. This initial startup for it takes a momentary large burst of power.
The burst of initial power has been stated to be so high that a florescent lighting is not "efficient" until it has been on for a short while.
Also there is a lot of interferance from a light of that type.
All of the above completly differs depending on the type of curcuits, start type, type of bulb and so many factors that even if I knew the exact model, I would not guess at how much power that would be.
The modern PC power supply has caps (power storage and cleanup) that can usually keep any very short burst like that from causing problems. Poor quality and older power supplies more likely to be effected from any short change in voltage from the wall plug.
Also you have interferance possibilities, the headphones wiring acting as antenna , any poor shielding , and a small burst of airborn energy.
If the audio device is a bluetooth type of connection, it woud be very typical that the data stream could have glitched , from interferance , and restarted, taking a bit of time to resend packets , fill buffers and all.
If it was either of the above things you could test for them.
For interferance, leave the lamp on the same plug and test with it further away from the computer and any extended wiring from the computer (IE the headsets).
For the power surge Power the lamp from a completly different wiring curcuit of the house (socket to the main curcuit box). A Different room sometimes, different sections of the house, then you could run a extention (temporarily) to put it in the exact same place, and see if it still did it.
To add more information, was it Wireless type? What is the Computer model? The PSU type? What is the model of the USB audio device? And what is the lamp item or bulb type?