This encyclopedia entry explains that
The Greeks and Romans did not attempt a work containing all the words of their own or any foreign language; their early dictionaries were merely lists of unusual words or phrases. [. . .] One of the earliest works in Latin lexicography, by Verrius Flaccus, is De Verborum Significatu (The Meaning of Words), compiled during the 1st century AD. This work, in which the words are arranged alphabetically, has furnished a great deal of information on antiquities and Latin grammar.
De Verborum Significatu is, unfortunately, mostly missing in its original form - edited and published not by Flaccus but by Sextus Pompeius Festus, who made edits and inserted some new comments and thoughts. He also changed the organization of the work, alphabetizing some of it. Various incomplete versions and updates have been compiled over the past few millennia since Festus published the first (see, for example, the 1839 edition), and they are, in general, in better condition. Information about a project dedicated to improving our understanding of De Verborum Significatu can be found here.
However, the work was not widely used. It was supposed to be a scholarly resource, and given its size (in full, it would have encompassed 40 volumes), it would have been impractical for an ordinary Roman to acquire a copy - or to make a significant number of copies, for that matter.