How suddenly does lactose-intolerance onset?
Disclaimer: I am not medically qualified, and this answer must not be construed as being medical advice of any kind.

Primary adult hypolactasia is the most common cause of lactose intolerance. The majority of the world's population have this phenotype. 

In these individuals, at weaning, there is a reduction in the level of the enzyme lactase, which is responsible for digesting lactose to galactose and glucose in the small intestine. Undigested lactose can create symptoms via osmotic effects (causing diarrhoea) and because it is metabolised by bacteria in the colon, producing gas and thus abdominal bloating.

About 35% of adults have a genetic variant in an region upstream of the lactase gene which results in the expression of lactase continuing into adult life. These individuals are lactose tolerant. This trait is most common in Northern Europe.

According to references cited in  


  Ingram, CJE et al. (2009) Lactose digestion and the evolutionary genetics of lactase persistence Hum Genet (2009) 124:579–591 


(I have removed citations from the passage for clarity.)


  "most lactase non-persistent individuals can tolerate small amounts of lactose (as in tea or coffee), and some can consume a lot without ill effects. Variation in the composition of the gut flora between individuals, as well as a psychosomatic component may account for some of the interindividual variation in symptoms."


The clear implication is that there is a lot of variation in the tolerance of lactose amongst those lacking the lactase persistence trait. Given the contribution of the gut flora to the symptoms these could presumably vary as a result of, for example, antibiotic treatment. Also I imagine that the effects of undigested lactose could be synergistic with some other gut disturbance.

Added in response to comment from the OP:

In someone with the (common) genotype that corresponds to 'no persistence of lactase' the possibility of showing symptoms will be present from a young age. Apparently there is a lot of variation in the severity of symptoms. If an adult suddenly exhibits symptoms then I am suggesting that this could be due to an interaction of non-persistence with some other gut disturbance - I imagine this could happen quite quickly. Alternatively I suppose that a change in diet could trigger symptoms.