This is a quirk of GFIs that doesn't happen very often but can happen. It's most frequently seen when running UPSs off a GFI outlet.
Don't listen to anyone who tells you to remove the GFI. They are necessary with saltwater tanks, for your protection and your livestock's protection. Every saltwater tank should have a GFI with a grounding probe, but a GFI (with no probe) at the absolute minimum. If something fails in that water and you stick your hand in while you are touching something else that's grounded, you will get a "hot to ground" electric shock which is one of the most deadly shocks you can get from residential power. GFIs are specifically designed to protect against this occurrence.
What is happening in your case is that the ballast in your lighting system causes an inductive kick in relationship to ground when the timer cycles off. The GFI is detecting that kickback as a ground-fault current and is tripping. It's all technical electrical stuff that isn't really important to know, but there are a couple of ways around it.
First, try placing a dedicated surge protector in between the plug to the lighting system and the timer. A big power strip isn't necessary, simple single plug units are available for 5 dollars or so from Lowes or Home Depot. See attached photo. These devices will tend to absorb the high voltage kick that occurs. This may or may not work.
Second, you can try moving the timer to the other side of the GFI, and placing a GFI after the timer. In other words, plug the timer directly into the wall outlet, place another plug in GFI unit after the timer, and plug the lights into that. By moving the timer, you place the kickback in a differnet part of the circuit that might keep the GFI from tripping. This also may or may not work.
As a last resort, it may be necessary to run the lighting system and timer without the GFI. I personally recommend that ALL equipment run off of it, but since your lighting system does not come into direct contact with the water, it's not as big of a deal to leave it off the GFI. However, this should be a last resort and you should leave all the equipment that is in contact with water (pumps, powerheads, heaters, etc) on the GFI.