LMM: LMM Falls on its face, then comes back when I let off and get back into it

[c20elephant]

My LBZ used to do the same thing till I fixed without using a lift pump, so use a lift pump, I'll be installing one someday...

 

[TheBac]

Lift pump would be my first thought.

 

[malibu795]

Low rail pressure. More diagnostics would be required to tell you what is causing it.

This..

Swap fuel filter, could've got a dirt tank of fuel doesnt take much to plug a stock filter with no lift pump
Put back to stock tube
Or
Get a lift pump

Have through a p0087 code yet?

 

[portmax29]

Mine would do the same, I installed the race plug on my 02 and fixed the issue. Granted i already had the lift pump and was running a higher tune than you are.

 

[RHallenbeck]

My 2010 LMM would do the same thing.. Installed a Lift pump and never had another issue..