I second the notion that OP is closest to the situation and best able to assess what specifically to do. Torrential downpours can be dangerous for visibility and lightning even more so. One can also get some clues from weather maps and reports on whether this is an intermittent phenomenon or longer lasting.
On my trip last month, there were forecasts of a front with ~3-5" of rain forecast moving through - though the timing wasn't 100% clear. The first day it was forecast for late afternoon, so I started in the morning and figured I would have a bail out option half way through if it became bad. Hence, perhaps an hour or so of cycling but not worse. As it turned out, it didn't really arrive until ~4am of the following morning so I was glad I got a day of riding in.
On the morning it came through, I figured I'd wait until 10am at latest to make a call. It was intermittent at times though not fully expected to clear until afternoon. I decided to take that day as a rain day. Glad I did. Even though it eventually became a beautiful day after 3pm or so and I could have had some hours of riding - it also would have been wet with not as much visibility before then.
However, circumstances and forecasts can vary a bunch...
As far as being caught in remote areas goes... my experience is many of the more remote areas in the lower-48 in the US are also arid. So they can get storms but it may not be as frequent. For example, on a trip across the ST, I had some windy days but not much rain in the drier areas. In Outback Australia I did get a rather big front coming through. I stopped mid-morning and set up my tent. The main front was fairly quick and two hours later, I packed up the tent and continued.
In Argentina, I started one morning with relatively light winds and what looked to be a reasonable day. A rather sharp front came through perhaps 15km into the ride. The wind picked up considerably and with it strong headwinds and a huge amount of dust. The dust storm really changed perspective and the winds made even pedaling some downhill pieces difficult. In that case, I soldiered on - but not quite as far as I otherwise would have ridden. So these arid regions I've definitely had other types of storm events that take some care.
