It sounds like you need to increase your Lantus (Basal), you should be able to achieve a reasonable morning without going too high. What basal/bolus ratio are you working with? 55-60% basal and remaining bolus working well for me. Maybe you need to reduce your bolus and increase your basal to improve your morning numbers and reduce the hypos. I would advise that first you get your basal sorted by basal testing. Basal testing involves testing when you wake up and skipping breakfast/lunch (testing every hour). As long as you remain within range the entire time without any major fluctuations then your basal rate is correct. If you become low/high stop the test and adjust.
Once you have your basal sorted you can begin to adjust your bolus by testing pre-meal and then 2 and a half hours after meal, testing 4 hours after a meal can be a good indicator for fatty foods and fine tuning. I believe you can also do bolus testing where you only eat breakfast and then skip lunch, watching for fluctuations (repeating for each meal). DP is fun and is experienced by many people; I always take the most amount of insulin per carb in the morning.
There is no right and wrong answer for this game we play so you will have discover the rules for yourself. Good luck!
