In Spanish, it's the first person subjunctive form of "to wash". So you'd use it to express something like "It's good that I am washing myself" or "Maybe I am washing it."
I don't know what subjunctive means so I don't know if you are right about that, but I am a native Spanish speaker, so I can tell you that those examples you gave using "washing" (a gerund, I think) would use the corresponding tense "lavando" in Spanish:
It's good that I am washing myself = Es bueno que me esté lavando.
(That's a literal translation: I don't think anyone would use "lavar" for washing yourself, more likely "bañando" [bathing] or "aseando" [cleaning] --at least not in Mexico, but what's idiomatic does vary quite a bit from country to country. Although for "wash your face" you would say "lávate la cara", using the verb "lavar".)
I am washing it = Lo estoy lavando.
Here are some sentences where I would use "lave" or "lavé":
Dile que lo lave mañana= Tell him/her to wash it tomorrow
Lavé las cortinas con agua caliente = I washed the curtains in hot water.
