The Collaborative International Dictionary of English v.0.48:

Elegize \El"e*gize\, v. t.
   To lament in an elegy; to celebrate in elegiac verse; to
   bewail. --Carlyle.
   [1913 Webster]

WordNet (r) 3.0 (2006):

elegize
    v 1: compose an elegy [syn: elegize, elegise]

Moby Thesaurus II by Grady Ward, 1.0:

27 Moby Thesaurus words for "elegize":
   bemoan, bewail, climb Parnassus, compose poetry, deplore, dirge,
   give sorrow words, grieve, keen, knell, lament, lisp in numbers,
   make immortal verse, moan, mount Pegasus, mourn, poetize, repine,
   sigh, sing, sing deathless songs, sing the blues, sorrow, verse,
   versify, weep over, write poetry