I'm not sure that running a bit too lean  *would* show up in a clean,
direct way, on the typical not especially strenuous emissions tests.
Running lean means that not enough gasoline is being put into the
mixture, in proportion to the air. It isn't good for your valves, and
on modern cars with closed-loop engine controls it means that
something has gone wonky with a sensor or two.

Running lean enough would show up as excess HC or (unburned)
hydrocarbons at the tailpipe.  Yes, fuel going unburned because of too
much air -- an engine is meant to work within a certain range, at that
temperature and pressure.     You might see it as high NOx (nitrogen
oxides) because of higher combustion temperatures as well.  (Running
*very* lean, possibly enough to cause driveability problems, can
decrease NOx, as I (mis)understand it, but sends HC through the roof
because of misfires.) Having the last smog slip around as a baseline
for comparison is helpful.

O2 and/or mass-airflow sensors are among the things to watch for in
your onboard diagnostics readout, if your car has them (what make,
model, year, and engine are we talking about?) and I guess so could
timing that is off beyond the computer's ability to twiddle it.

Are you talking about a tailpipe test or a code?

the injector is pumping a bit too little gas, which makes the NOx
levels go up on the readout. Normally engines today run a teeny bit on
the lean side, to keep the HC and CO levels down, but a twinge further
and that's what you get. It's relatively limited, however, since a
twinge further than that, and it won't run at all. As with all mixture-
related things, the first thing to try is replace the exhaust sensor.
Other possibilities, however, include low fuel pressure from a
clogged fuel filter, clogged injectors, clogged fuel lines, bad fuel
pump; bad computer, etc. But most likely, the exhaust sensor, followed
by the fuel filter, both of which need to be replaced every once in a
while anyway.