Question

Is there any way lack of rain might strain English relations with the Powhatans

Answer 1

Answer;
Yes, it would affect both, there would Less food to go around

Explanation;
The way that lack of rain might strain English relations with the Powhatans is that there would be less food to go around.
Lack of rain would affect both. It reduced corn supply. Hungry people tend to be more aggressive and this might cause more fighting. The lack of rain would have made it difficult for native settlers to do farming, and therefore, there would be less food in the region 

Answer 2

One could argue that a lack of rain would have strained English relations with the Powhatans, since this would have made farming much harder to the naive settlers, which would have forced them to rely on the good-will of the Natives more.