I have the same problem in single player not using the mod.
I discovered a solution, but in your case it's not going to work, you will have to have a cold start.
In single player, when it is working, go to the RIO position. Their you will see that the LIQ COOLING switch is on the off position. You can turn it on. The LANTIRN is going to work.
When you land and rearm and refuel and turn off the LANTIRN you will have the same problem. To solve it go to the RIO pit and switch off the LIQ COOLING switch, turn on the LANTIRN. As soon as the LANTIRN is on, put the LIQ COOLING switch on the on position.