Short answer, no, it's not natural. If we're speaking about the future, we say "when the rain becomes (or much more commonly "gets") lighter, I will go out." If you're not referring to the future, let me know the time (past, present), aspect (perfect, frequentative / habitual), and mood (real, possible, alternate reality) -- and I'll give you some more help, Ms. Cherry.

There are two issues with the sentence, the overall grammar and the usage of "lighter." Regarding the grammar, you should say, "When the rain becomes lighter, I will go out." "Would" would only be used if the sentence were conditional, ie uses an "if". Note also the verb form for "become" needs an "s" ending. Where I come from, I'm not sure we say "lighter" when talking about rain, but they may other places. In central US, we might say, "When the rain lets up a bit, I'll go out." or "When it stops raining so much, I'l go out."