Green’s Dictionary of Slang

lumber (sauce) n.

[SE lumber, wood]

(US) a toothpick.

[US]H.W. Bentley ‘Linguistic Concoctions of the Soda Jerker’ in AS XI:1 44: Lumber. Toothpick.
[US]P. Kendall Dict. Service Sl. 11: Lumber...toothpicks.
[US]WELS [DARE].
[US] in Newark (OH) Advocate 21 May 3/3–4: lumber -- toothpicks.
[US] in DARE.