Is a good idea to inform potential PhD Advisor that I sent my application for joining his lab?
If that makes you feel better, sending a quick email is probably fine. Something along the lines of:

Hello Dr XXX,
I have just submitted my application to program Y, as you have advised. Looking forward to hearing back from them!
Best,
Student

Even if you don't get a reply, a quick note like this should be sufficient to remind the professor that you are still interested in his lab. Good luck!