It is possible to create a pseudo 3D lidar with a 2D one. You have to add a motor or more specifically a servo that tilts the LIDAR. You can then continuously tilt the LIDAR and just integrate all the measurements together to form a 3D point cloud. If you look at this paper you can see an example of how they set this up in Fig 2. You can also use that paper as a reference for building your LIDAR mapping software.
Other papers you can take a look at with open source implementations are
BLAM,
HDL graph SLAM,
and many more just google LIDAR SLAM or LIDAR mapping.
Also you do actually need a proper 2D LIDAR to do any sort of mapping. From your post it looks like you have this https://buy.garmin.com/en-US/US/p/578152 which is called a LIDAR-lite, but is basically just a range finder.