Here is a remarkable read: With the Tibetans in Tent and Temple: Narrative of Four Years' Residence on the Tibetan Border, and of a Journey Into the Far Interior, by Susie Carson Rijnhart, M.D. The dates are 1895-1899, which causes some revision on our "first" lists. Seems they left America for Tibet in 1894.
Unfortunately, this book was written by a Christian missionary. That she rather tragically lost her husband and only child on this venture did not soften her view of Buddhism in general and Tibetan people in particular. Still, I do not perceive her as a fanciful liar, and while the picture she paints of the Tibetans and their lamas is less than flattering, it is interesting nonetheless.
The whole book is online here. Definitely worth a visit.