"Study" as you say is not the typical meaning in Classical Latin, at least when it has an object. When it lacks an object it fits better with the sense of "study." So I suppose you could say "Litteris Latinis lectis, studeo" where instead of an object you employ an ablative absolute or abl. of respect.
It is better thought of as an emotional state rather than an action. Which is why it frequently attracts a dative object (thing):
M. vero Catoni, homini ignoto et novo, quo omnes, qui isdem rebus studemus ... (Cic. Rep. 1.1)
Omnibus modis huic rei studendum ... (Caes. Gal. 7.14)
Same when it attracts a dative indirect object (person), in this case dear old Catiline
quamquam multi boni adulescentes illi homini nequam atque improbo studuerunt
(Cic. Cael. 4.10)
Rarely, it can attract an accusative object, but those uses still have an emotional quality and they mostly occur in poetry, and a couple times when Cicero refers to a whole concept (quod) as an accusative object.
As for the absolute use of studeo that is where you will find it to have a more "study" sense.
Non est [ratio], quod post cibum studeas. (Sen. Ep. 94, 20)
meaning "there is not [a reason] why you might study after food [=eating]"
From the L+S:
Absol.: “neque studere neque odisse,” Sall. C. 51, 13.—
B. To apply one's self to learning, to study, be diligent in study (only post-Aug.; for which in Cic. litteris, arti, etc.; v. supra, I. A. δ): “computamus annos, non quibus studuimus, sed quibus viximus,” Quint. 12, 11, 19; 2, 7, 1: Demosthenes diligenter apud Andronicum studuit. id. 11, 3, 7: aliquem a proposito studendi fugare, id. 2, 2, 7: non est, quod post cibum studeas. Sen. Ep. 94, 20: “duo, qui apud Chaldaeos studuisse se dicunt,” id. Q. N. 7, 4, 1: “negat enim te studere,” Plin. Ep. 7, 13, 2: “studes an piscaris?” id. ib. 2, 8, 1; 2, 13, 5; “5, 5, 18: solacium studendi,” Suet. Tib. 61: “videtur mihi inter Menenios et Appios studuisse,” Tac. Or. 21; so id. ib. 32; 34.—Subst.: stŭ-dens , entis, m., a diligent student: “in habitu studentis,” Plin. Ep. 5, 5, 5.