Yes that is true, logistical support and processing have considerable costs. For aerial LiDAR collection via helicopter you're looking at about $20,000 per day of onsite collection including the helicopter team, insurance, and support. That gets you high density low altitude assets, not including the processing and storage costs.

It's cheaper to fly with a fixed wing aircraft, but you will typically get lower density assets and the possibility of obscured imagery due to cloud coverage because of the higher collection altitude. However the advantage is you're able to cover a wider collection swath with each pass, and it's a lot easier to fly a fixed wing vs. helicopter so the pilots are cheaper.

How much would the total weight be for the lidar equipment? I wonder if drones would be able to significantly reduce the price.

That depends a lot on the density of point coverage you need. Most LiDAR receptors weighed between 100-300lbs five years ago. They have become much smaller now, again due to self driving cars. However I am not sure that the hardware which is suitable for self driving applications would be "survey grade" appropriate for forest canopy and ground truth mapping. I'm also not sure what the power requirements of the newer LiDAR arrays are, but the weight for batteries is significant as it directly impacts your time "in the air" between ground support stations. In a helicopter you can power all the instruments off a DC power supply from the turbine.

Also typically you want an absolute vertical accuracy of +/- 5cm during flight in order to confidently map the surface features below foliated vegetation cover. This requires quite specialized differential GPS equipment as well as a radio/cellular connection to a commercial GPS ground station network. With the improvements in GLONASS/GALILEO constellations maybe the ground networks are not as critical anymore.

Met a Cal archeology ass’t prof doing this, quadcopter-mounted lidar.