One of the uses of the present perfect is when you are talking about something before now and that exact time in the past is not important.
"I have travelled a lot" is one example using your example. Your travel is in the past (before now), but the exact specific time of that travel in the past is not important. Maybe it was a lot a week ago, maybe it was a lot a year ago, etc.
When you use the continuous tense, you want to give the listener a sense that this 'event' went on for a period of time - it had a duration. It wasn't something that happened quick and then was over.
Using your example again, "I have been travelling a lot lately." gives a sense of the time duration of this travelling in the past. The listener can visualise you travelling over a period of time, and not just an instant in time.
'lately' is not necessary for the present perfect continuous. It's just used as a time market to tell the listener that this travelling was recent and not further back in time.