I am so glad you are considering this topic.  (I would shift the wording from lonliness to 'social isolation' since social isolation puts the problem in its social context and does not individualize it (YOU are lonely...it is your problem).

As for studies with elders I do not know of any - that does not mean they do not exist. But there are studies of the deleterious effects of social isolation - many done in regard to 'solitary confinement' used a punishment....studies of isolated babies, children etc. 

If your research were to show a connection between lonliness (psychological isolation) and dementia, I think it could have practical effect in those cultures where the old are isolated...where others have low expectation of them...where they are excluded from valuable service eg. grand parenting ,  mentoring etc.