For-Profit to Non-Profit to For-Profit H1B?

Hi everyone. I am currently on H1B working for For profit company. Recently a recruiter reqch out to me with good offer for non- profit org, they are willing to sponsor H1B.

If I go on non-profit H1B, will I have to go through lottery process again in future if I decide to switch back to for-profit position?

Thanks in advance.