According to the second edition of the SBL Handbook of Style (2014), citing a volume or work in the Loeb Classical Library requires only the primary reference.
For the proper abbreviations of Greek and Latin works, see pages 141-168 in the SBL Handbook of Style.
Referring to a Text
If you are referring to a portion of the text in the second volume of Josephus' Antiquities or in Tacitus' Annales, you can simply type one of the following:
Josephus, Ant. 2.233-235.
Tacitus, Ann. 15
Quoting a Translation
If you are quoting the translation of one of these volumes, you would include the translator:
Josephus, Ant. 2.233-235 (Thackeray, LCL)
Tacitus, Ann. 15.18-19 (Jackson, LCL)
Bibliography
The bibliography entry for these would be as follows:
Josephus. Translated by Henry St. J. Thackeray et al. 10 vols. LCL. Cambridge: Harvard University Press, 1926-1965.
Tacitus. The Histories and The Annals. Translated by Clifford H. Moore and John Jackson. 4 vols. LCL. Cambridge: Harvard University Press, 1937.