If you even so much as approach the insurance company on your own, I think you would serious damage, if not destroy, any possible case you may have. Insurance companies rely on and are sticklers for contracts, not on being nice guys. As a matter of economics they can not and will not pay claims they have not agreed to pay and are not obligated to pay. Lots of people lapse their policies, for lots of reasons. Some die the day after the lapse occurs, and companies don't pay.
If you go to them and ask "can't they just" overlook the lack of payment for an understandable reason, or won't they please pay a small part, they will simply say NO. And they will take your request as definitive evidence that there is no basis for a claim. Further in your request to the company you may make admissions that will harm any claim you had.
Then even if you get a lawyer, and the lawyer finds a strong legal basis, or perhaps an arguable basis to establish some right on your part to the proceeds, as they will have essentially made the decision earlier they will do everything in their power to assert the earlier decision was right, that you and the lawyer are bluffing, and act accordingly.
There may be some basis for contending the insurance did not lapse for lack of the premium payment. It all depends on the type of life policy, the policy wording, the exact facts and in some cases the state and insurance company. (In other cases it sometimes depends on the lawyer you have -- and a lawyer who is an expert and respected -- if not feared -- by the company and insurance defense industry can do far better for you than any old lawyer.
If such a a lawyer who specializes in insurance would be willing to take your case, the lawyer would probably work on a contingency basis -- no fee unless the lawyer recovers for you -- if there is any possible basis for a claim. But whatever you do, don't approach the company without a lawyer.
