This is the right way to compare strings:
int studentCompare = this.lastName.compareTo(s.getLastName());
This won’t even compile:
if (this.getLastName() < s.getLastName())
Use
if (this.getLastName().compareTo(s.getLastName()) < 0)
instead.
So to compare fist/last name order you need:
int d = getFirstName().compareTo(s.getFirstName());
if (d == 0)
d = getLastName().compareTo(s.getLastName());
return d;