Hi Rehaf.
I see it like this: the liver has glycerol kinase not only to trap glycerol for TG synthesis, but also to turn it into glucose during fasting state, that's its function (one of many, of course).
The adipose tissue in the other hand is mainly for storage, it uses the excess of glucose and VLDL to synthesise TG to meet this purpose, so it doesn't really need the enzyme for that.
I don't know if that makes sense to you

, I hope it does, it was just a way to simplify it for me.