Technically you're right, the LM002 wasn't directly built for the US Military but the
LMA002, LM001, & Cheetah was. It started with the Lamborghini Cheetah in 1977 then the [one] LM001 by 1981, they were both prototypes for bidding on the US Military defense vehicle contract...the first HMMWV (equivalent to the Hummer H1) was built in 1979, see the coincidence?
The center of gravity using the AMC V8 in the LM001 was too high resulting in bad handling so the V12 from the Countach was used in the front of another chassis putting it much lower and they called it the LMA002. By the time the LMA002 was complete in 1982 the contract for 50,000 HMMWV's at already been awarded to AM General and Lamborghini lost out.
Ever seen a BMW M1? Lamborghini screwing around with military vehicles and not winning the contract is what killed the BMW M1 project. BMW commisioned Lamborghini to assemble them but they had no money due to the above vehicles: people don't understand how much in the automotive industry revolves around racing, even alot of the day to day street cars now...
Then you have Jeep trying to sue AM General over the HMMWV because they used the same amount of bars in between the headlights as the jeep grill for decades BUT being military vehicles they are excempt from patents, copyrights, & trademarks...sooo much politics which lead to major lawsuits when the civilian Hummer came out in the middle 90's and the lawsuits continued between Jeep and General Motors with the H2.
Anyways, between 1986-1993 300 or so of the LM002's were built with most of them being ordered by middle eastern military's.