Is it correct?

What would you do in that situation?
I would pray that the lion wasn't hungry.

IMGIs it grammatically correct to use "was" in that sentence?

Yes, or at least it is common enough. 'That' suggests a situation that is past. 'Isn't' would be fine, too. I think it is a matter of the speaker's momentary perspective, that is all.

I thought that if the part of the sentence before "that" is in the past tense, everything that goes after "that" should be in the past, too.
For example, "she said that they went to the office". Could this rule be applied in this case? "I would pray that the lion wasn't...".

However, I always get confused about this rule. I think there are situations when

IMGI think there are situations when one can say "she said that they are in the office" - right now they are in the office. Could you comment it, please?

Generally, if the situation still obtains at the time of speaking or if it is a general truth, then the subordinated verb needn't regress with the main verb—though it usually does.

Thank you, you helped a lot!