Monitor your bg for a couple of nights to see what happens, it might be that you need to increase the night-time dose but it could also be down to the Dawn Phenomenon. There's also the possibility that your bg is going low during the night and your waking bg is the result of the rebound (Samoygi Effect), either way you won't know unless you check your bg.
As for going low at lunch, make sure it is your basal and not your breakfast insulin, try skipping breakfast one morning and see if your bg continues to drop before lunch-time, if it does then you need to reduce your morning basal dose, if it doesn't drop then your breakfast insulin to carb ratio is wrong.