Can I run an LS3/L99 swap in a '96 Tahoe on the old 0411 PCM?

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

• E40; LS2, LS4, 5.3L; 2005-2006: Per EFILive's PCM application spreadsheet, E40 (24x crank, 1x cam) applications include the 2005 Corvette LS2, 2005-2006 GTO LS2, 2005-2006 SSR LS2, 2005-2006 TrailBlazer 5.3L, 2006 TrailBlazer SS LS2, and 2006 Impala SS / Monte Carlo SS LS4. (EFILive (forum-hosted))
• E38; LS2, LS3, LS7, LS9, L92; 2006-2011: Per EFILive's spreadsheet, E38 (58x crank, 4x cam) applications include 2006-2011 Corvette LS2/LS3/LS7, 2010-2011 Camaro 6.2L, 2008-2010 G8 6.0L, 2007-2010 Avalanche/Suburban/Sierra/Silverado, and the 2010 Corvette ZR1 LS9. (EFILive (forum-hosted))
• E67; LS2, 5.3L, 4.2L I6, 3.5L/3.9L V6; 2006-2009: Per EFILive's spreadsheet, E67 (58x crank, 4x cam) applications include 2006-2008 V6 cars (Malibu, Impala, G6, Aura), 2008-2009 TrailBlazer/Envoy 4.2L I6 (exhaust cam VVT), 2007-2008 TrailBlazer/Envoy 5.3L, and 2007-2009 TrailBlazer SS LS2. (EFILive (forum-hosted))
• E40; LS2; 2005-2006: Some LS2 engines were built as Gen III variants (24x); the spreadsheet notes engine codes 5MC, 6MC, YTA, ZJA, and ZJB as examples, citing other sources. (EFILive (forum-hosted))
• 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, E67, T43; LS2, LS3, LS7, LS9, L92, truck Gen IV V8, 4.2L I6;…: The E38 and E67 ECMs introduced for 2006 use a Motorola PowerPC 40 MHz 32-bit RISC processor with 2 megabytes (2048 KB) of flash and were the first GM controllers with floating-point processing. The E67 adds input/output lines over the E38, making it the choice for variable valve timing applications. Six-speed automatics got the T43 TCM, which is mounted inside the transmission with the valve body. (GM High-Tech Performance / MotorTrend)
• E40, E67; 2005+: The E40 and E67 controllers both have three connectors, but the pin counts differ and the units do not interchange; the proper harness and sensors must be used for each specific controller. (LSX Magazine)
• E38, E67, E78, E92; Gen IV V8; 2006+: E38, E67, E78, and E92 controllers were also used on engines besides V8s, but they can be reprogrammed for a Gen IV V8 (except the Gen V E92) as long as the programming inside the box is known before first start. (LSX Magazine)
• Gen III PCM (P01/P59); LS2, LS3, LS7: A Gen IV engine (LS2, LS3, LS7) can be run on a Gen III (LS1-style) controller if the 58x reluctor wheel is swapped for the Gen III 24x wheel and adapter harnesses are used for the cam position sensor and throttle body, because throttle body operation is reversed between the two generations; some sensors may also need replacement. (LSX Magazine)

Confirm against the instructions for your exact parts before wiring. More: Computer and tune in our tuning guide.