Facile persuādet Lucumōnī ut cupidō honōrum et cui Tarquiniī māterna tantum patria esset. The translation I have reads, “She had no trouble in persuading a man who was eager for distinction, to whom Tarquinii was only his mother’s birthplace.”
What is ut doing in this sentence? It doesn’t seem to be signaling a purpose or result clause.
Ut means “as” here, or “considering that”. A literal translation: “She easily persuaded Lucumo as someone eager for distinction and as someone for whom Tarquinii was only his mother’s birthplace.” “She had no trouble persuading Lucumo, considering he was eager for distinction and Tarquinii was only his mother’s birthplace.”
Ut can be used this way with an indicative clause, or with just an adjective or some other expression not amounting to a full clause.
Ut has many uses. Here is the relevant section of Lewis & Short’s article on ut:
b Reflecting the assertion to particular circumstances, etc., ut = for, as, considering: hic Geta ut captus est servorum, non malus, Ter. Ad. 3, 4, 34: ut est captus hominum, Cic. Tusc. 2, 27, 65; Caes. B. G. 4, 3: Themistocles ut apud nos perantiquus, ut apud Athenienses non ita sane vetus, in regard to us, etc., Cic. Brut. 10, 41: Caelius Antipater, scriptor, ut temporibus illis, luculentus, for those times, id. ib. 26, 102: nonnihil, ut in tantis malis est profectum, considering the unfortunate state of affairs, id. Fam. 12, 2, 2: (orationis genus) ut in oratore exile, for an orator, id. Or. 3, 18, 66: multae (erant in Fabio) ut in homine Romano, litterae, id. Sen. 4, 12: consultissimus vir, ut in illā quisquam esse aetate poterat, Liv. 1, 18, 1: florentem jam ut tum res erant, id. 1, 3, 3: Apollonides orationem salutarem, ut in tali tempore, habuit, id. 24, 28, 1: Sp. Maelius, ut illis temporibus praedives, id. 4, 13, 1: insigni, ut illorum temporum habitus erat, triumpho, id. 10, 46, 2: Ardeam Rutuli habebant, gens ut in eā regione atque in eā aetate divitiis praepollens, id. 1, 57, 1: vir, ut inter Aetolos, facundus, id. 32, 33, 9: Meneclidas, satis exercitatus in dicendo, ut Thebanus scilicet, Nep. Epam. 5, 2: ad magnam deinde, ut in eā regione, urbem pervenit, Curt. 9, 1, 14: multum, ut inter Germanos, rationis ac sollertiae, Tac. G. 30. —
http://perseus.uchicago.edu/cgi-bin/philologic/getobject.pl?c.19:370.lewisandshort
Thank you very much, Qimmik. I never thought to take ut as “as” and cupido as dative of cupidus. I would not have understood this sentence without your help.
Two different uses of ut in a line of Vergil, Ecl. 8.41, neither with subjunctive:
ut uidi, ut perii, ut me malus abstulit error.
“When I saw her, how I perished, how an ill delusion swept me away.”
Qimmik is, I believe, Hylander in a former incarnation. 
I won’t confirm or deny.