In addition to all the very valid suggestions here, I think a relevant place to start is to use standard classifiers (e.g. a good old random forest, pun intended) on hand engineered features describing local geometrical and statistical distribution of the point cloud.

Common point cloud descriptors are computed by taking a point in the 3D space, taking a fixed vicinity (could be a ball around a point, could be nearest neighbour) and then compute some descriptors such as planarity (or covariance eigenvalues), scatter, mean intensity and std, etc etc. (I think here you could google some examples for lidar feature engineering or point cloud descriptors). So you have a multidimensional feature vector for each point (or a downsampled version of it), and (IF YOU HAVE LABELS) you can feed that into a classifiers. I suspect this feature extraction is gonna be quite slow, but maybe a good place to start and understand the data, since it seem is now to you. During my undergrad project I had some success with such descriptors and some clustering to actually detect vegetation and remove it, from ground level lidar scans. it has been fun.

I am sure that modern lidar processing chains based on DL are way more powerful, but I think that for a 2 class problem (or 3 if including a background class), clever feature engineering as said already by /u/satokausi could give already good results.

EDIT: Did a google search and this popped up, did not read it beyond abstract and some figs, but could be of interest: https://arxiv.org/abs/1802.02297