Parsing inflected forms may not always work as expected. If the following does not give the correct word, try Latin Words or Perseus.
per-lĭbet or -lŭbet, ēre, v. impers., it is very pleasing or agreeable, I should very much like: colloqui, Plaut. Capt. 4, 2, 53: scire, id. Rud. 2, 3, 23.
Hence, perlĭ-bens (-lŭbens), entis, P. a., doing or seeing a thing very willingly, i. e. with good will or pleasure: ausculto perlubens, Plaut. Trin. 3, 3, 50; 4, 3, 34: me perlubente allisus est, to my great delight, Cic. Q. Fr. 2, 6, 6.
Hence, adv.: perlĭbenter (per-lŭbenter), very willingly, with great pleasure, Cic. Univ. 1; id. Att. 8, 14, 2; cf. id. Fam. 7, 14.