I don't know anything about laser designators.
What happens when they light up a target? Do they automatically give up their position? I thought I read somewhere it was only an issue that they don't want you to light up a target because you have to put your gun down, not that it gives away your position.
I know a few things (I used them often back in the day). They do not give away your position (except you have to be a bit more exposed to get on target). You do have to choose between the laser and your primary weapon though which in an active firefight is not a choice to be made lightly.
Also, and this is the biggest thing - YOU DO NOT USE ONE UNLESS YOU HAVE ASSETS AVAILABLE. What that means is there was SOMETHING in the immediate AO that could utilize the laser to target.
It could have also been a laser for calculating GPS coordinates utilized in GPS guided munitions such as a cruise missle, JDAMs, etc.
One way or another that operator believed strongly enough there was a use for determining the position of the mortar team, strongly enough that he put down his primary weapon and lite the target up.
Then he was left to hang out to dry and died.