From Dictionary.com based on Random House Unabridged 2006:
Logistics [Origin: 1875–80; < F logistique quartermaster’s work, equiv. to log(er) to lodge, be quartered (said of troops) + -istique -istic; see -ics]
Lodge [Origin: 1175–1225; ME logge < OF loge < ML laubia, lobia; see lobby]
Lobby [Origin: 1545–55; < ML lobia, laubia covered way < OHG *laubia (later lauba) arbor, deriv. of laub leaf]
Leaf [Origin: bef. 900; ME leef, lef, OE léaf; c. D loof, G Laub, ON lauf, Goth laufs]
From American Heritage Dictionary of the English Language, 4th Ed
Logistics [French logistiques, from logistique, logic (perhaps influenced by loger, to quarter), from Medieval Latin logisticus, of calculation; see logistic.]
Logistic [Medieval Latin logisticus, of calculation, from Greek logistikos, skilled in calculating, from logistēs, calculator, from logizesthai, to calculate, from logos, reckoning, reason; see leg- in Indo-European roots.]
Trouble in paradise, eh?
I invite general comments.