How was the diversity between ethanol fermentation and lactic acid fermentation evolved?
First, it is not clear from the physiology or biochemical information alone to determine what evolved from what. The intermediate pyruvate is always there, so lactose dehydrogenase (LDH) and pyruvate decarboxylase (PDC) could have each evolved anytime, and there are good reasons for both:


LDH: the reaction pyruvate + NADH/H+ = lactate + NAD+ + 25 kJ/mol is highly exergonic, i.e. produces heat
PDC: the reaction pyruvate = acetaldehyde + CO2 (and with ALD present) acetaldehyde + NADH/H+ = ethanol + NAD+ where ethanol is poisonous to other species


Add to it that there are organisms like Sch. pombe that have both enzymes, so can do both reactions, your questions should be rather:

How has the enzyme LDH evolved?

The enzyme is similar to malate dehydrogenase, both form a family. They belong to a group of enzymes that all have a NAD(P) binding domain, so it's not too far-fetched to state that LDH and MDH evolved from another enzyme with NAD(P) binding domain.

http://www.ebi.ac.uk/interpro/IEntry?ac=IPR016040

How has the enzyme PDC evolved?


  Protein sequences of pyruvate decarboxylase (PDC) derived from cloned
  yeast (Saccharomyces cerevisiae) and bacterial (Zymomonas mobilis)
  genes were compared with each other and with sequence databases.
  Extensive sequence similarities were found between them and with two
  others: cytochrome-linked pyruvate oxidase from Escherichia coli and
  acetolactate synthase (ilvI in E. coli; ILV2 gene in S. cerevisiae).
  All catalyse decarboxylation of pyruvate using thiamine pyrophosphate
  (TPP) as cofactor. General overall similarity suggests common ancestry
  for these enzymes.


cited from abstract of

Green, Jeremy. "Pyruvate decarboxylase is like acetolactate synthase (&lt; i> ILV2) and not like the pyruvate dehydrogenase E1 subunit." FEBS letters 246.1 (1989): 1-5. http://www.ncbi.nlm.nih.gov/pubmed/2651151?dopt=Abstract