how likely to be successfull losing weight on insulin

Background:

Diagnosis of Graves Disease in 1996 with unsuccessful thyroid eblation.

Left untreated until 2005 when dramatic weight loss and increased thirst occurred.

Diagnosed type 1 in 2005 at age 42.  Simultaneous rediagnosis of Graves Disease. 

Successful thyroid eblation again in 2005 at the time of diabetes diagnosis.

No diabetic family history other than a grandfather.

5'2" 140 pounds from 109 pounds at 2005 diagnosis

Very restricted diet of less than 15 carbs/day and 0 sugar because I don't want to be put on further insulin for fear of further weight gain.

Questions:   

Any chance of losing weight while on insulin? Lantus 12units; Synthroid 100 mg.

Are there any "natural" remedies that help with type 1?

Any chance that the Graves Disease contributed to the onset of the diabetes?