I will fly Philippine Airlines from LAX to MNL in March, 2022. I hold a Business Class ticket. Will I be allowed to stay in the Star Alliance Lounge in LAX before my flight?

I would still try or see if you can get a day pass, even a discounted one. I would try through Philippines customer service since you have business class they may direct you even to another lounge.

When I flew Philippine Airlines Business Class May 2022 I was able to avail the Star Alliance Lounge.

Just pay the $60 USD for 3 hours option

Unfortunately as PAL is not member of star Alliance.. it's unlikely you will be able to get in