There is no fundamental limit to how many points you can process when gridding in MapInfo Advanced. I have tested with hundreds of LAZ files containing several billion returns successfully.
I suggest you use the Triangulation gridding method for large lidar datasets. You could also use Nearest Neighbour if the output from that was suitable for your purposes.
Make sure you use the lidar return filtering options to make sure you grid only those returns that suit your requirements.
Pro will read in all the point data and cache them in a temporary file that will be placed in your temporary file location. You might need to make sure you have plenty of disk space there and it is best if it is on an SSD.
As it will take a long time to ingest the data and grid, you should do some trial runs on a subset of the dataset first to work out exactly what gridding method parameters and what raster geometry parameters (like cell size) you want. For Triangulation, make sure you set the 'maximum triangle size' large enough to fill holes, but not so large as to create long slivers on the edges. Keep it tight.
For large jobs like this I recommend having 32 GB of RAM. You can have the source files on a HDD but its best if temporary files and the output file are on an SSD. Write to MRR format if possible and if you want some other format it is best to convert the MRR to that format afterwards. If you have a CPU with more than 4 cores, that's good. Finally, have patience. You are asking your machine to do a lot of hard work and it will take time.
I have plans for two optimisations that will make handling large lidar gridding operations easier and faster. Firstly, there is a secret setting in the Triangulation method that is not exposed in the user interface. It can improve gridding performance significantly (at the expense of using more memory) and I plan to expose this in the next version. Secondly, I may allow users to retain the point cache file so you only have to read the source data in once, and then can grid from that saved cache as many times as you want. That would streamline the workflow for these very large point datasets.