I will contest this, I have had a wideband on my truck at KRC Performance. With CAI and Tuner with a Performance tune on my truck already, the addition of LT headers all worked to lean me out quite a bit. Not CEL lean, but fairly close.
Marty suggested I go to a 180* thermostat to keep the truck in closed loop, in which, the PCM will richen the mixture slightly (just as happens when your truck is warming up.
Worked for me, the change to the cooler thermostat brought me almost up to bone stock, factory A/F ratio.
I have NO numbers with just a CAI and performance tune (both act to lean the mix, one via more air entering the TB, the other by advancing the timing) but since my truck was still not lean enough to produce a CEL with LT headers as well, I don't think you are so lean that you NEED one.
For me, it's a band aide, since the only real way for me to richen the A/F would have been to get a piggyback A/F controller or a custom tune. The $20 thermostat is a much cheaper solution...