There are 2 ways to complete with: Sticky Bombs or Sniper Rifles. You will have 90 seconds to set up however you want to do this.
Sticky Bombs need to either get onto Lowery's SUV or an adjacent car. The easiest way to do this is to drive a car in front of the hotel and park it in front of Lowery's SUV. Throw a sticky bomb underneath the car and retreat to the garage. If you plant the bomb on or by Lowery's car early, there is a high chance his body guards will spot it and the mission will fail. Wait for the checkout timer to expire and for Lowery to get into his car. Once the headlights go on, detonate the sticky bomb. You will likely have a 1 Star Wanted Level. If you want to blow up Lowery directly, it gets a lot harder.
To get Lowery directly you need to wait. As the car is leaving the Von Crastenburg Hotel, then you want to lob a sticky bomb onto it. After it rolls off a ways, then detonate it. If you are not in visual range, there is a chance you will not even get a wanted level.
This is the easiest way to handle the mission, plus it nets you extra money. Trigger the checkout timer and head for one of the higher levels of the parking lot. The second level is a good choice. The top level offers a Stunt Jump escape as well, with a little set up.
Once you are in position then you need to wait for the Check out timer to expire. Lowery will not be too long in leaving the hotel now:
Target him and take him out before he gets into his car.
Move back from wherever you made the shot.