Llevo mucho tiempo viviendo aquí 'I've lived here for a long time' shows a very common use of the verb llevar.
It has various meanings including 'take', lead' and 'wear'.
It is also used in the present tense (as in the sentence above) with the meaning of having passed time somewhere. There is no literal English translation. Llevo mucho tiempo viviendo aquí could equally have been translated as 'I've spend a lot of time living here'.
The Days of the Week.