This can be addressed using the following LINQ expression:
var result = peopleList2.Where(p => !peopleList1.Any(p2 => p2.ID == p.ID));
An alternate way of expressing this via LINQ, which some developers find more readable:
var result = peopleList2.Where(p => peopleList1.All(p2 => p2.ID != p.ID));
Warning: As noted in the comments, these approaches mandate an O(n*m) operation. That may be fine, but could introduce performance issues, and especially if the data set is quite large. If this doesn’t satisfy your performance requirements, you may need to evaluate other options. Since the stated requirement is for a solution in LINQ, however, those options aren’t explored here. As always, evaluate any approach against the performance requirements your project might have.