A friend of mine is having driving lessons.
Can I ask him both?
How long have you been having driving lessons?
or
How long have you had driving lessons?
Often, the present perfect is quite flexible in this type of situation. You can use the progressive form, or not. For example:
I have lived here for 10 years
sounds just as good as
I've been living here for 10 years
However, certain situations (and certain verbs) require a little more care. In your example, the second option sounds horribly clunky. This is because you are using the verb "have" to mean "do/perform/execute", which are dynamic uses*. As such, you will need to use the present perfect progressive form to highlight the repeated/regular action of "doing driving lessons". (Imagine that driving lessons take place on a regular basis, say, weekly.) As such, the correct option is
How long have you been having driving lessons?
*(If you were using "have" to mean "own/possess" (a stative use), then the situation would be different: How long have you had your dog?)
'Have' cannot be used in the continuous form when it means 'own' or 'possess'. So, you must say 'How long have you had (owned) your car?' 'Do you have a pet?' 'I have a lot of friends'. This is because 'have' with this meaning is a stative verb - it describes a state or condition.
'Have' can be simple or continuous when it is an active verb - it describes and action. This is seen in expressions such as 'have a coffee', 'have a good time', have a shower' and so on. e.g. 'They are having dinner' - describes the action of eating. 'My neighbours are having a party' - describes the actions of dancing, listening to music, eating, drinking, etc.
