With all of the nice detailed specifications, the key performance of gaming is the graphics card, and that Lenovo has Graphics NVIDIA GT 730 2GB
Although there are a few versions of the card, a GT 730 is a fairly low performer.
Lenovo generally uses adequate but low wattage power supplies, so that PC probably needs a new power supply and graphics card upgrade.
GT 730, depending upon its version is about a GT 940M laptop level.
http://www.notebookcheck.net/...849.0.html
It should therefore play at medium settings and on 1080p should be about 40fps
http://www.game-debate.com/...-gt-730-v2
You can build a slightly better system for $521. There are low performance power supply, motherboard, and computer cases in purchased branded systems like the Lenovo.
http://pcpartpicker.com/p/D9NjdC
$130 upgrade GTX 750 TI and better power supply gets it close to a PS4 performance.
$155 upgrade GTX 950 and better PSU gets it above a PS4
Real gaming computers start as on sale at $500
http://www.newegg.com/...6883102038
AMD FX-6300 (3.5GHz)
8GB DDR3 | 1TB HDD
Nvidia Geforce GTX 750 Ti 2GB
CM Storm Devastator KB/MO
The FX-6300 is nowhere near as gaming strong as the i5-6400
Core i5-6400 @ 2.70GHz score 6491 in 4 cores and 4 threads
FX-6300 Six-Core score 6346 in 6 cores with shared resources
Non-gaming is close to the Lenovo, and you will get low frame rate sequences in GTA V from the FX-6300, but this PC does high settings in the 40's average fps
$570 ending today GTX 950 FX-8320 better computer case, plus wireless
http://www.newegg.com/...6883227507
Again, the 8 core AMD has gaming instability in many games, but non-gaming beats the Lenovo performance and gaming is over five times the performance of the Lenovo.
And here are the core i5's at Newegg
http://www.newegg.com/...30537+4814
Generally, upgrading the power supply fixes any issues with a purchased PC, and then gaming is mostly the graphics card. Good power supplies can be figured out, or ask for help:
https://pcpartpicker.com/parts/power-supply/#e=6,5,4,2,1&sort=a9&page=1
http://www.realhardtechx.com/index_archivos/Page2293.htm
http://www.realhardtechx.com/index_archivos/Page362.htm
CPU + GPU general scoring: http://www.videocardbenchmark.net/gpu_list.php