How many letters can be excluded and still produce a recognizable lipogram of Mary's Lamb? For starters, excluding five letters jkqxz has no effect as they're absent in the original. Excluding five more letters bfpvy had a minimal effect, as see here (substitute words underlined).
"A Backdoor Approach to Lipograms,"
Word Ways: Vol. 44
, Article 4.
Available at: http://digitalcommons.butler.edu/wordways/vol44/iss1/4