Which is a better sedative for sleep and anxiety, diazepam or lorazepam? What's the difference. Haven't been sleeping well My 0.5 lorazepam isn't helping much so doc gave me script of 2m diazepam.

Therapy? Have you yet tried any form of psychotherapy? Typically, the optimal combination of things to treat emotional issues such as anxiety or depression is medication (which, on your best day, is supposed to take the edge off symptoms) but the real gruntwork takes place in psychotherapist's consulting room.
Meds for sleep. People have unique responses to these medications, so you will benefit most if you keep sleep diaries, filling them out first thing in the morning. Record the time the medication is taken, dose, time you went to bed and other details. Take the diaries with you when you talk to your prescribing doctor. CBT for Insomnia is considered the gold standard though, for treating insomnia long term.
Sleep disorder / Anx. Both are Benzodiazepines but the major difference is the onset of the drug. Diazepam (Valium) Rapid onset Lorazepam (Ativan) intermediate onset. By giving you a 2mg Valium he actually lowered your dose. .5mg Ativan= 2.5mg Valium. If you take this med throughout the day I would suggest prescribing Ambien (zolpidem) 10mg for sleep and Klonopin .5mg twice a day or as needed. .
Insomnia, Anxiety. I understand your concern of not sleeping well Lorazepam and Diazepam are medications for Anxiety, they are not sedatives The effect of lorazepam lasts for 6 hours, and effect of Diazepam lasts for 8 hours. Both medications are habit forming Stresses of relationships, separations, work, finances, unresolved conflicts can cause sleep problem. See a Psychiatrist for Diagnosis, medication and therapy.
Depends. on the situation. For long term Diazepam is good last longer, half life 20 to 80 hrs. as out pt t/t. For short acting Lorazepam is better half life is 10 to 20 hrs.