I have worked in wireless communications for 30 years and have worked on GPS timing at wireless sites. At one time, i was responsible for inspecting, approving, and repairing grounding systems at these sites. First, if you install a surge arrestor, any surge arrestor, you must ground it. That ground MUST be bonded to your main entrance ground. If not, you just created a ground loop and another source to ground through your equipment.
The method we used for lightning protection started at the tower top. The coax cable shield was grounded to copper bus bar that was electrically bonded to the tower structure via solid tinned #2 wire cadwelded to the tower itself. At the base of the tower, there were one or more cadwelded #2 wires going to a buried ground system. Even the tower ground has to be bonded to the main service entrance ground. Before the coax was routed inside the base station shelter, the shield was again grounded to another copper bus bar bonded to the earth ground system. Inside the building, just below where the cables come in, another copper bus bar this is where the surge arrestors would be mounted or grounded to.
This bar is also bonded to the earth ground. It was about 24 inches by 4 inches and was pre drilled with holes for mounting wire terminals. This bar, has a layout. On one side surge Sources were attached ( surge arrestors). The middle of the bar was the Absorber and another solid #2 was cadwelded to the bus bar and routed to earth ground system. The other side of the bar is where equipment grounds were connected. The thought on this is that a surge is taking the most direct route to ground. By putting the absorber between the surge and the equipment, the vast majority of the surge is routed through the short route to the absorber.
A surge, such as a lightning strike, is taking every path to ground. Proper grounding gives a low impedance path to route most of that surge safely to ground. Wires, straps, etc should be direct and always routed downward. A surge doesn’t change direction well, so don’t snake the wires up and over things.
Back to the GPS in your lab. Chances are, you aren’t going to put your antenna high up, just in a mostly open area. You could probably do fine without the surge arrestor, but if you want the reassurance, make sure it’s grounded properly and no surge arrestor is better than one with its own isolated ground rod.
I have a spectrum analyzer that uses a GPS reference for timing. It has about 15 feet of RG174 ( I think, same size) and works fine. You may be able to put a piece of foam in a window and close over it.
On my ham station, I used to use a piece of aluminum sheet in a window and put coaxial barrel/bulkhead connectors through it. This way you attach a male connector on each side. It served the same purpose as the outside ground bus bar in my description. It was about 3 inches tall and cut to fit the window opening. The window was just closed over if.