First of all, don't worry about raising your doubts in this forum because the objective is precisely that we all learn from the problems and solutions that others raise with their own data. The advantage of this is that none of us are born experts, and the more knowledge is shared the more it grows. I can assure you that the learning curve (and I have been teaching my students with LAStools for many years) is very smooth and the truth is that the program allows large projects.
My first recommendation is that you always associate the projection system within the LAS/LAZ file itself to avoid later problems. Effectively this is done through LAS2LAS and particularly for me the most comfortable is to use the EPSG of the desired CRS. If you want to check if the file has the system well defined, besides being able to use QGIS to check it, you can use lasinfo that gives you a complete information of the data.
If you want send an example file (in LAZ format to reduce the size) and what would be your desired projection system (EPSG code) and I will send you the corresponding commands and a brief explanation.
Greetings and we continue advancing,
*** We will continue making LAStools bigger.