I am looking for a dataset combining both lidar point cloud and individual tree inventory (positions, crown diameter,...) on a forested area.
There are a few websites that you can go to
https://en.wikipedia.org/wiki/Lidar Look at the External Links at the bottom
I haven't found a site that combines both tree inventory open data and LiDAR open data. You might have to compare the coverage of a number of unrelated sites and hope they coincide.
For LiDAR open data a good portal is OpenTopography, you can download small areas. I would encourage you to create an account as this will increase your download limit.
The US Interagency Elevation Inventory is a great portal as well. It will direct you to external data repositories but the coverage is awe inspiring.