I just bought a beauty 2001 suburban and would like to buy nice new shoes for it. it's stock car and I was thinking to put 20" rims with 285/55R20 Terra Grappler tires and would like to get anyone's opinion if these wheels and tires would be ok without installing the lift kit. Thanks in advance for your opinion!!!

 

Been done several times by properly using a 9"x 20" Rim. Your overall diameter is going to be 32.5" which you'll have to just deal with on the Speedometer and other issues related to a larger tire.

Just make sure that the Rim Manufacturer guarantees that the Rim you select/they recommend for your specific vehicle, has sufficient offset where the Tire won't scrub/rub.

PS:
Burbs are Trucks, not Cars

 

Welcome to the forum.

Also make sure that your wheel will clear the calipers.

 

Should be fine, but like said gettin the proper rim is key. Width a offset play a big role in what tire size will fit without trimming

 

If you get some minor rub on the wheel house plastic liners, you can reshape using a heat gun instead of just cutting them.