As I understand it, the lean burn capability is pure electronics; nothing to do with the cam profile. The computer figures out the right conditions (which I am sure are related to vacuum (via MAP sensor), engine speed, vehicle speed, etc) and cuts the fuel and then monitors the lean burn via wide range O2 sensor (aka Lean Air Fuel (LAF) sensor).
There is a way to monitor that, according to a thread that TomO put together at GasSavers.org:
Civic VX Lean Burn monitor - GasSavers.org - Helping You Save at the Pump.
The SOHC VTEC-E (as it's called on the VX) works kind of the opposite direction as a typical VTEC... (again, explaining this as I understand it so apologies if I explain it poorly) The VTEC-E minimally opens the 2nd intake valve at low engine speeds to better help mix the air & fuel (and therefore allow leaner burning at those speeds) and then gradually goes to normal 4-valve operation at higher engine speeds (the ECU definitely can still allow lean burn even at the higher engine speeds). On the other hand, the standard (SOHC) VTEC opened the intake valves normally at low engine speeds and then opened them even more at higher engine speeds.
Apparently, there is also a 3-stage VTEC which combines both the economy of the VTEC-E as well as the performance of a SOHC VTEC... but that one was never made available in the US market.