Can a live in POA forbid family members from taking the parent out of home for simple lunch or day trip?

If the person they are POA for is still mentally competent the answer is NO, the person is allowed to leave with other family members if they want to. However if the person is no longer competent then the POA needs to act in their best interests and at this current time, it may not be in the persons best interest because of COVID, if the person has dementia being removed from their environment may be stressful and cause undue harm.

RobinBH, we need information as your profile hasn't been filled out yet. What are the health issues, if any, for the parent? Does the parent still live on their own? Or is the parent residing in a senior facility? Or in your home?

With the covid-19, I can't believe someone would want to take an elder out into the world. I wouldn't even take myself out for a simple lunch or a day trip. With a day trip, bathroom stops are needed. Why risk it?

Depends on the authority created and granted in the document.