Not quite. What are you trying to say?
For the same meaning as the previous sentence, you could add "as" or "when" before "I". The construction is a little strained as "last time" refers to "as I was driving here", but it is common enough in speech.
If you mean that there has been no rain since the time you last drove here, you need "the" before "last time" to remove any doubts of ambiguity in what is rather an unusual coincidence. You don't need "the" in your original sentence (not when spoken at any rate), because the meaning is obvious and expected.
Both raining and driving can be expressed as continuous events.
Many choices that people make in choosing tenses are arbitrary, Fbohn. I can't think of any clear rule to guide you here.
I would be most likely to say "The last time I drove here, it was raining." When I choose that version, I view the driving as one action that doesn't need to be expressed as a continuous or ongoing action. I view the rain as an ongoing event that took place as I drove.