Luke Henry didn't know why his bothers left him he only knew that they joined the military so Luke joined the military because he wanted to follow in his older brothers foot steps he looked up to Batok more than Elliot. While in service he found records of where his brothers where sent to Chernarus knowing the dangers of Chernarus he wanted to find a way into the city to find his brothers and be reunited brothers. he eventually found a boat it was in bad condition and barely usable he got some materials to make it stable enough that he can use it.
he knew it was going to be hard to find his brothers. Luke kept his head up and eventually found his way to his brother.