the best way to avoid the battery draining is to unplug your Luke when you arent playing and the life span is usually pretty decent I have a str*t with EMGs in it and I changed the battery out about every few months (not that I have actually touched that guitar in years haha)
Here is info about the Petrucci (not Luke, sorry) that I found on the Music Man FAQ;
The battery life of course will vary depending on how much your guitar is plugged in. Whenever your guitar is plugged into either jack, the battery is under load. The average battery life is about 4 months for the player who practices every day for about an hour and gigs 1-2 times a week. One way to remember is: whenever the season changes - so should your battery.