There is, what do these words mean? and, would a native speaker say it like that?
"sometimes we're together all the time."
This would have the meaning, there are periods in the year when we're together most, if not all of the day. It is not specified how long this goes on for, whether for days at a time, or weeks or what.
Because it uses "times" twice, a native speaker would avoid using a sentence like this.
Sometimes we're together a lot.
Now and then we spend a lot of time together.
what about "always": sometimes we're always together.
I can't think of a sentence to provide any context that I can 'force' this sentence into. As it is, a native speaker just would not say this.