Can an adult without genetic lactase persistence still develop a tolerance for dairy foods?
It seems that yes, it is possible to increase the tolerance for lactose over time, and it has to do with the adaptation of microbiota.

A simplistic explanation comes in the following article: 
 Hertzler SR, Savaiano DA. 1996. Colonic adaptation to daily lactose feeding in lactose maldigesters reduces lactose intolerance. The American journal of clinical nutrition 64: 232–6.

In which the authors claim the following: 


"Colonic adaptation appears to reduce the symptomatic response to lactose via several mechanisms. (...)
(...) increased β-galactosidase activity after regular lactose ingestion indicates that colonic bacteria are able to ferment lactose more rapidly. (...)
(...) This metabolic shift is thought to result from the proliferation of lactose-fermenting, non-hydrogen producing organisms such as Bifidobacteria."


This article makes reference to another one which supposedly explains the microbiota adaptation:
Hill Mi. Bacterial adaptation to lactase deficiency. In: Delmont J, ed. 1983. Milk intolerances and rejection. New York: Karger: 22–6.

But unfortunately I could not find the full text. I hope you are luckier than me.