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Just a quick try,do you have smart key app?
Kind of,when on smart key and having call option,sometimes the keyboard doeesn't pop up in a call.
Just restart your device regularly (every 3-4 days) and it should be better. If not,you can try a software repair.
Well thre is a lag in the keyboard app ... for that i suggest you to use "Google keyboard"
and for menu lag there might be a little bit of it but shouldn't b very big .. if its too much check maybe you have too many running apps or push notifications ....
how much free ram do you usually have ? after say 4 hours of use ?