The Collaborative International Dictionary of English v.0.48:

Lank \Lank\ (l[a^][ng]k), a. [Compar. Lanker; superl.
   Lankest.] [AS. hlanc; cf. G. lenken to turn, gelenk
   joint, OHG. hlanca hip, side, flank, and E. link of a chain.]
   1. Slender and thin; not well filled out; not plump;
      shrunken; lean.
      [1913 Webster]

            Meager and lank with fasting grown.   --Swift.
      [1913 Webster]

            Who would not choose . . . to have rather a lank
            purse than an empty brain?            --Barrow.
      [1913 Webster]

   2. Languid; drooping. [Obs.]
      [1913 Webster]

            Who, piteous of her woes, reared her lank head.
                                                  --Milton.
      [1913 Webster]

   Lank hair, long, thin hair. --Macaulay.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Lank \Lank\, v. i. & t.
   To become lank; to make lank. [Obs.] --Shak. --G. Fletcher.
   [1913 Webster]

WordNet (r) 3.0 (2006):

lank
    adj 1: long and thin and often limp; "grown lank with fasting";
           "lank mousy hair"
    2: long and lean [syn: lank, spindly]