Insert points into a 2d grid
Technically, this is a mathematical modelling problem. You just happen to be using earth science data - satellite LIDAR readings.

Ore reserve geologists constantly deal with this, but in three dimensions when they are required to create a block models of a geological deposit from drill hole data.

Scientific fields that use 2D data would include: forestry, meteorology and ground contamination studies looking into pollution effects of smelters.

Methods you need to consider are Inverse Distance Weighting and possibly variography and kriging. Variography and kriging are elements of geostatistics, also known as the Theory of Regionalized Variables.

With inverse distance weighting, the distance variable is usually raised to a power n, i.e. ${1/d^n}$. Choosing the appropriate value of $n$ is the tricky part. When geologists used inverse distance weighting, prior to primary using geostatistics, typically the value of $n$ used was 2, but values between 1 and 3 have been used for different deposits.

Given that you are using two dimension data, you may need to use GIS software or other modelling software that offers grid interpolation methods, such as I have mentioned to achieve what you want.