I agree with the fact he may be a 3k-5k guy with a strength in speed vs his endurance. However, you are asking how he can improve his training for the mile.
You are look at ABOUT 12-14 weeks left of real/focused training before States, correct?
Has he ever been in a weight room?
I would do a few things:
#1. Try not to let him run faster than his goal mile race pace at the moment for his workouts. As a previous poster commented, it's a bit early for that and he WILL get tired when it counts.
#2. You have enough weeks left to see physical adaptations to resistance training which can have positive effects on power and rate of force development for the 100-1600meters especially.
#3. Don't over race him during indoors.
But back to the resistance training, I would try and put together a PERIODIZED plan that has him progress through 2 phases. Each cycle can be about 6 weeks long. The first 6 weeks should focus on endurance strength and be slightly higher in sets/reps and also include an EASY introduction to plyometric work and efficiency drills.
Some lifts to focus on would be:
bench press
dumbbell arm swings
dead lift
front squat
russian dead lift
calf raises
walking lunges (with dumbbells)
single leg squats
cleans (ONLY if you are familiar with the lift and feel confident introducing it to him; if not, I would not include this because it's better to avoid injury and keep it simple)
For light Plyometrics, have him do about 30 meters of the following drills for 2 sets the first 2 weeks, then increase to 3 sets for the remaining 4 weeks:
bounding
a skips
b skips
high knees
box jumps
split squat jumps
For the 2nd phase (weeks 6-12) I would recommend lowering the reps and increasing the weight to closer to 85-90% RM. You would be looking at sets of 3 X 3 or 4 X 3 depending upon the lift and how he is responding. He many need more rest but the goal of this phase is to focus on strength an power and explosiveness. The difficulty of the plyometrics
should also increase.
The key to this type of training is to continue through the indoor season and not worry if he is not PRing or setting the world on fire. It will take a minimum of 6 weeks to let the body physiologically adapt to the training before you start to see drastic improvements. The goal is the be CONSISTENT but also allow for recovery. He should not be lifting more than 3 days a week, esp. if he is new to the lifting. Also , make sure he is eating properly and fueling adequately to allow for maximal recovery and adaptation. If you don't do the little things, the effort put into this type of program can cause overtraining effects instead of being positive and helping to maximize running economy and speed.