Can a 4L80E be controlled by the factory E38 PCM/T42 TCM setup in a truck that originally had a 4L60E?

Here is what the documentation says. Each point links to its source; details depend on your exact computer, harness and transmission.

Transmission control

• The Quick 4 includes a separate input-shaft-speed-sensor connector that is used only for 4L80E applications; 4L60E/65E/70E transmissions do not use it. (US Shift)

Computer and tune

• E40, T42; LS2, LS4, LH6, 5.3L truck V8; 4L60E/4L65E/4L70E; 2005-2006: The E40 ECM was used only for the 2005-2006 model years. It controls the engine only; transmission control was split off to a separate stand-alone T42 transmission control module, also flash-based with 1 megabyte of memory. (GM High-Tech Performance / MotorTrend)
• E38, T42; LS2, LS3, LS7, Gen IV truck V8; 2005+: The E38 is a Gen IV engine-only controller with two connectors; like all Gen IV controllers it relies on a separate transmission controller. For the 2005 Corvette, GM scrapped the single-PCM concept in favor of separate engine and transmission controllers. (LSX Magazine)
• E67 (Chevrolet Performance); LS3, LS7; 4L60E/4L65E/4L70E: Chevrolet Performance Automatic Transmission Controller 19302405 is pre-programmed for 4L60E/4L65E/4L70E transmissions, provides full transmission function after connections with no laptop programming required, but is only compatible with E-67 based Chevrolet Performance electronic LS engine control systems. (Pace Performance)
• E67 (Chevrolet Performance); LS3, LS7; 4L80E: Chevrolet Performance Automatic Transmission Controller 19302410 is the pre-programmed variant for the 1993-up 4L80E family, likewise compatible only with E-67 based Chevrolet Performance engine control systems, with RS-232, USB, and CAN 2.0b communications and on-board data logging. (Pace Performance)
• T42; 4L60E/4L65E/4L80E; 2006-2014: T42 TCM retail application data: part 24255280 (T42 hardware) covers 2006-2014 Express 1500 4-speed applications and interchanges with 24230461, 24234503, 24235340, 24239224, 24239926, 24241806, 24243901, and 24252114; part 24241806 is listed for a 2009 Silverado 6.0L with generic number 24252114. (Highway 71 Auto Parts)

Confirm against the instructions for your exact parts before wiring. More: Transmission control in our tuning guide.