[Alamo-Girl]

Thank you so much for your post!

Up to now, I know of no "naturally occuring" number which has been proved to be normal. All constructions of normal numbers that I'm familiar with (and I don't think I've missed many) are "lexical" in nature.

It appears the editors at MathWorld agree with you with only three exceptions which are probably "lexical" as you say:

Normal Numbers

Strangely enough, with the exception of a number of special classed of constants (e.g., Stoneham 1973, Korobov 1990, Bailey and Crandall 2003), the only numbers known to be normal (in certain bases) are artificially constructed ones such as the Champernowne constant and the Copeland-Erdos constant.

Lurkers: Korobov is explained on the link and these two appear to be related:

Stoneham Number

Bailey and Crandall

[Doctor Stochastic]

If you analyze the expressions carefully, Stoneham's construction is "lexical." He carefully arranges things so that there is littly carry between terms. Similarly for bailey and Crandall.