the verb llever as an auxiliary is used like in English the tense present perfect continuous.
This is true but does not mean that the English "has/have been doing ..." can always be expressed in Spanish by "llevar + gerundio". There is an additional restriction on the Spanish usage (that does not exist for English) i.e. there also needs to be an expression of "measure of time". In the English translation this will almost always take the pattern "have been doing X for 'time-expression'".
The measure/duration can be quite precise ("LLevo 23 minutos estudiando.") or quite vague ("Llevas mucho tiempo escribiendo.") but it needs to be a measure of time. Thus it's fine to say "LLevo veinte años viviendo aquí.". However the English "I've been living here since I was five years old." would be "He vivido (or just "vivo") aquí desde que tenía cinco años." ("llevar" won't work here).