LADA and type 1 are the same thing.
There is no clinical diagnosis of LADA/1.5. It's just autoimmune type 1 diabetes.
The thing that may make you LADA or type 1.5, rather than just referring to yourself as type 1, is a particularly long and strong honeymoon period. Most type 1 diabetics will have a honeymoon period, that is a time when they have residual insulin production going on. The honeymoon period can make blood sugar control a bit easier because your pancreas still makes some insulin in response to food, or it can make it more unpredictable because the endogenous insulin production happens in fits and starts. Those diagnosed as infants/children tend to have a short lived honeymoon period and they stay on insulin treatment throughout, those diagnosed older may have a longer honeymoon period and still stay on insulin. Some people with LADA may have such a strong honeymoon that they are able to come off insulin for a while - but this will only be temporary as with type 1 your immune system is geared up to kill off your insulin producing beta cells and it will kill them off, even if it takes a while.
So if you're over 30, diagnosed with type 1 and commenced on insulin straight away you're not really LADA or type 1.5, you're just type 1. Even those who do refer to themselves as LADA are type 1, just with a stronger honeymoon period. Age of diagnosis doesn't make you LADA it would be the honeymoon period that would determine whether there's any point in thinking of yourself or referring to yourself as LADA - if you're on mdi with a basal bolus regime there probably isn't.