Lantus Question

My son, Sawyer gets 1 unit of Lantus at dinner.  He is 2 1/2 yrs. old.  He used to be on NPH and was taken off because of the peaks were so unpredicitable.  My question is what is a good number around 12pm for him to be because I am afraid of not catching a low.  For example, last night at 12pm he was 135 and then at 1pm he was 113.  So therefore I was afraid of him dropping from 1-5am so I gave him 3 oz. of milk and then this morning he was 181.  While I know these numbers are within his 80-180 but it could be better and was until I gave him the milk.  Can you please shed some light on how Lantus works!  Is there a slight peak 6 hrs. after injection and is there a slide through out the night?

Thank You in advance!