Ha, knew mechanical engineers that didn't know how to change a tire or electronic engineers that didn't know how to use voltmeter, so much for engineers.
Throttle lag is defined as the ability of the TB vane to follow the accelerator pedal, with more information, sure doesn't sound like your problem. Given advice on modifications will give you more noise, but won't solve your problems either. Bad advice, tune, if lucky, maybe a couple of extra HP, but will have to use the very highest octane fuel you can find, this varies like crazy all over the world.
Older vehicles actually had a built in dynamometer to let you know instantly how your engine was performing with an AT. With service brakes on, wheel blocked in low gear, just floor the gas pedal to learn if you could hit 1,800-2000 RPM, if you did, your engine was in top performance.
DO NOT TRY THIS WITH THE CRAP THEY ARE MAKING TODAY, WILL TOAST YOUR AT!!!!
With used vehicles with driveability problems, sounds like yours first tool is a compression gauge tester, when expecting 150 pis per cylinder may read around 80, these need a good carbon cleaning and a prayer. Some will go up to 150, others down to zero, carbon actually can help compression.
The way engine parts are today, really kick this around to look at the rest of the vehicle, you can't buy a complete engine overhaul gasket kit for four bucks anymore, will be over 150 bucks just for a head gasket. And gaskets were always the cheapest parts!
Had to give this bad news to my brand new daughter-in-law, just married, just out of college, student loans, her dad and I got her something she could drive. And she more than paid us back with three of the most wonderful grandkids in the world.
Next step if the engine is even running is to connect a real oil pressure gauge, stupid things won't light the low oil light if the pressure is above 3 psi. If you go to a quick oil change place, that charges your for a new filter, may learn it wasn't changed in the last 50,000 miles or so, even caught dealers pulling this BS. Engine has to be flushed to clean out all the crap, again, hope and prayer the oil pressure goes way up, look for around 40 psi.
Ignition is cut and dry, clean plugs, good connectivity, check the internal resistors, proper gap and torque. With only one vehicle, had to make my own timing marks, CAS was under the harmonic balancer, bracket was bend, initial timing was way off.
Another valuable is a spark plug gap tester, inconvenient on the Cruze, have to lay the module on its side, pull the boots and jumper each terminal to each individual plug. Plugs are in the head for this test, just substitute each plug one at a time, cutting the engine each time and expect to see a spark going across a 1/4" gap on the tester. Only for a few seconds, have to worry about your cat, but not much of a problem when its cold, worthless when cold. Will get a misfire code, that can be cleared with a scanner.
Another need tool is a fuel pump pressure gauge, at idle should see 45 psi, and with the engine off, that 45 psi should hold, some even for a month, others a couple of seconds. Low pressures could be excessive voltage drops to the pump, or even a plugged fuel filter. Leak downs can be anywhere, but with injectors, will find a wet cylinder. If Seafoam doesn't clean them, can be removed and manually cleaned. Have a procedure for this in lieu of a $7,000.00 injector tester. Ha, have all the stuff I need to do the same thing here. This is a long procedure, will have to post it separately.
Daughter had throttle lag due to dragging brake pads, good thing this was caught very early before rotor and pad damage. Not even related to the engine.
Another useful tool is a vacuum gauge, friend came over after laying out $1,600.00 from his dealer for parts he didn't even need. Took less than five minutes, a couple of his intake manifold bolts were loose. Never was a problem before with cast iron, sure is with plastic.
Can't cover anything in a short post, but you have a problem. IC engine has not changed in over 120 years, SOS.