The ride takes anything between 10 to 20 minutes, depending of area of the suburb you are going to.
If you are going to Lapad from any other area including from Gruz, where main bus station and ferry terminal is located, you can take any suitable bus line to Batala and then change to no 2 or no 6 to proceed further to your destination.
It is good to note that there are some areas in Lapad (like Batala or Montovjerna) that are much closer then others so they can be easily reached by foot from either Gruz or Dubrovnik Old Town (15-20 minutes walk)
Lapad is relatively new part of Dubrovnik, not as old as Dubrovnik’s Old Town.
Have a look at the photo of penisula which I took from the plane while flying over Dubrovnik on the bright, winter day 🙂 – note – the bay on the photo is Uvala Lapad Beach