Lunalilo is a bit tricky.
I think he's aware of the situation surrounding the Island's position, and he did try to make a treaty with the USA over Sugar.
So if he lives longer, he might figure that out without getting Pearl involved.
If he can manage that, then it's probable the USA becomes important to the nation's survival and support.
On that note, the Missionary party would probably be much more accepting of his rule, given that he wanted to reform.
It might not completely prevent the overthrow, but I think it would diminish it.
Remember Kalakaua took full advantage of his power to dismiss and make new cabinets and ministers, and it made a lot of powerful folks angry.
I don't see Germany getting anything. they're too far away, and I sincerely doubt Lunalilo would trust them. the British Citizens in the Islands liked Lunalilo better, so that might have some bearing on who he goes to.
As for Kalakaua, His situation is very precarious if Lunalilo continue to live.
I don't really know who Lunalilo can marry, but most believe that if he got the chance, he would have made Queen Emma his heir, thus pushing Kalakaua further out of the running.
Bear in mind the only reason Kalakaua got in is because he was elected. I think it's possible he might do a similar tour, if Lunalilo doesn't have children.
He's still in the running for being elected king.
I'm actually more interested in the Cultural effects a longer Lunalilo would have.
Remember, Hula and other traditional practices got a revival under Kalakaua. Lunalilo was also an avid songwriter, and he had written the first Anthem for Hawaii.