Well, first of all I would have to ask whether there were other avenues to getting out of military service rather than just lying. So, I can't actually give an opinion on that until there is more information. I have a relative who, in order to not go to Vietnam, became a conscientious objector, fought it in the courts, won and was able to do 2 years of home service. Steve was also investigating, during the Vietnam War, how to get out of military service if he was called up. He had a friend in the military look into whether he could also serve in different ways. So, there are other avenues to avoid military service, rather than just lying - even if lying seems easier.
Usually, I will always try to see if there are any options to avoid telling an untrue statement, and if there are, I'd rather go in that direction. However, again we need to look at the intention behind what we do. Especially since your reason appears to be a conscience objection to war. If you have a particular skill, sometimes this will aid you in using that skill in a different way than just military service in the sense of being a soldier and this involves service which is better Kamma than lying. So investigating into these avenues is also very helpful.