It's because Google is banned in China. It's purely political reasons and nothing to do with quality of Lenovo phones. You got the "t" version of this phone, that's meant for sale and use in China, specifically China Mobile's TD-SCDMA network. The international versions of the A388 all have Google Services.
You can't just sideload Google Services, won't work that way. Phone has to be rooted, maybe a custom recovery, Gapps package correctly flashed, etc. About doing this, I've got no ideas, not for this phone.