Based on the standard set in New Jersey v. T.L.O., are random checks of school lockers constitutional?

The Supreme Court's decision in this case does not
directly address the legality of random searches of lockers.  In fact, the Court's
opinion says

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We do not address the question, not presented by
this case, whether a schoolchild has a legitimate expectation of privacy in
lockers...

However, the case
does give some hints as to whether such searches would be
legal.

The major holding in TLO is
that students do have 4th Amendment rights at school but that those rights must be
balanced against the school's need to maintain order and a good learning environment. 
The task at hand, then, is to determine whether random locker searches are needed to
maintain a good learning environment or whether they are too
intrusive.

It is likely, given TLO,
that it is legal to bring a dog through the school to sniff at closed lockers.  It is
clear that schools do have an interest in reducing drug use and this would not be an
intrusive way to determine if drugs were present.  If a dog detected drugs at a
particular locker, there would be enough probable cause (in a school setting) to conduct
a more intrusive search of a particular locker or
lockers.

Overall, then, TLO, does not
specifically tell us if random locker searches are legal.  However, it is likely that
unintrusive searches like those conducted by drug-sniffing dogs would be legal while
random checks that involved opening the lockers and going through their contents would
not be.