This is usually assocated with degraded copper or trunks at the outside plant. Sometimes inside wiring if it's in really rough shape can cause this, especially with unterminated runs or incorrect grounds at the NID but it's less likely due to how short of runs the home wiring can have. For this case, I'd say get a Verizon Tech out to see if they can locate a potential problem with your copper loop. It's probably the best thing to do in this case. Make sure you insist that the problem is not due to your speed or the modem or the computer, they'll try to blame that first in many cases.
By the way if you have Voice service and see noise on that during thunderstorms, call voice repair instead of DSL repair. They will be the better choice since Verizon has to maintain quality service on the voice end of things, in addition to repair them when trouble is reported. DSL issues will typically be fixed when Voice service is fixed.
