You talking 270 @ 050 I take it? I'm mainly talking too much overlap. Stage 2? Is that 1/3 race? Or 1/2?
Just kidding. Not knowing what brand you have I am going to assume a truck cam will be fine, unless its a cam for a truck pulling motor, in that case, it likely will need "assistance". The more overlap, the higher the RPM needs to be for it to not get tricked into thinking it's lean from the overlap letting the intake air mix into the exhaust at low RPM, which the O2 sensor sees as lean, and it tries to correct, but it can't.
So as you get more overlap, the trick I like to use is to limit the learning below a certain RPM, up to 2500 RPM depending on the cam, so that it can only remove fuel, and not add it. 0% on fuel adding below that RPM. Then limit the closed loop correction to a small amount, maybe 10% or less on the addition. Then you have to tune below that RPM manually. But with a standard cam, say right around 230 duration @ .050" or below, it will work just fine for the most part. But it does depend on the whole combo, LSA, engine size, etc. Also, this is not a set number or a cutoff, its just about where it can start to cause issues at lower RPM above that duration, below 1500 or something. But again, its more about the overlap, not the duration. For EFI I like to keep the LSA at 112 or above NA, for forced induction then 114-118 depending on the combo. Although if you want a rough idle, a peaky motor, or have a carb then I go lower on the LSA.
Also, when you are tuning at low load cruise, where you can be almost stoich, but I still wouldn't unless its a MPG queen, 14 to 14.7 isn't going to matter much to be honest. Although I wouldn't run it at 14.7 anyway, as stated in the previous sentence.