You can find benchtop picoammeters in most major
test instrument mfrs' product lines although they are
a niche function.
You could build your own with an op amp and
precision resistor, transimpedance style and use
a generic DMM on the output voltage. Need to
get a good CMOS or JFET input op amp for high
Zin, and perhaps some care with PCB design.
A really crude option is a precharged capacitor
and timer, I=C*dV/dt. Take an open socket reading
to get at any fixture current which would be
superimposed. You could use a 'scope probe
(although its 10Mohms will perhaps dwarf the
leakage current of interest) to get the time for
dV=1V, or whatever.