Im so sorry about your dog's condition and her untimely end. I know this can be heartbreaking. I have gathered some information as I am not intimately familiar with the medication she was given accidentally. It seems that that does is below that which would be expected to cause a fatal arrhythmia but we do not know what role her heart condition played in all of this. The dose that she received appears to be lower than that expected to cause a cardiac event but this is healthy dogs, data involving dogs with pre-existing cardiac disease is lacking.
I can tell you that as a veterinarian that specialized in emergency and critical care, I do not consider heart disease to be a contradiction to inducing emesis, each case has to be evaluated on an individual bases, but I cannot recall a time when I have forgone this simply because of heart disease or a heart murmur (diagnosed or not). Its a risk benefit analysis and perhaps the vets at poison control didn't recommend emesis because they felt that the dose was low risk (but not "no" risk). Perhaps there is information we are missing as to why emesis as not induced? Maybe the calculated dose she was given was actually less than the dose received?
I have found an article on this toxicosis in veterinary magazine and here is the link http://veterinarymedicine.dvm360.com/lamotrigine-toxicosis-dogs-and-cats?pageID=3
Even with the induction of emesis, there is no way to know if your dog would have survived. It is possible that the toxicity was a red herring and there is some other reason she passed away suddenly- meaning that she would have arrested with or without the lamigotrine on board.
If you want more answers, I recommend having her body submitted to the the state or city/county veterinarian for a complete necropsy including histopathology. I will look more into this tomorrow as I am headed to bed tonight after a long overnight shift and staying up all day is this is all right. If you want someone to get back to you sooner, just let me know shortly and I will opt out so that your question will be open for another expert to address if one is available to answer it sooner. I promise to not be offended, I know that it is difficult to wait for information when you're upset.
In the meantime, I would like to commend you on doing everything within your power to have your dog treated appropriately. She was lucky to have a such quick thinking and dedicated owner, regardless of the sad outcome. I do not think that you did anything wrong, in fact quite the opposite, you did everything right from consulting poison control to taking her in for treatment right away.
Please accept my deepest sympathies for your loss.