Free speech is a modern concept. There were no laws in Rome giving a right to speak without being punished. Conversely, there were not too many laws against speech either. There appear to have been some civil remedies against defamation, but the evidence for it is slight and by all appearances it was difficult to sue someone for libel or defamation (see "Roman Law and the Legal World of the Romans" by Andrew M. Riggsby for more information).
We have only fragmentary remains of Roman law to go on and what can be gleaned from literature, so in many cases we don't know exactly what Roman law was or exactly how it was enforced (see Riggsby again). Other than the Augustan dicate against lese majeste, I don't know of any specific laws either allowing or outlawing speech. Even lese majeste itself, was not specifically about speech, but more about any act that would be insulting to the government.
Imperial Rome was a dictatorship and the emperor had the power to arrest or kill people without a trial, so laws were mostly meaningful only in a civil context. When it came to criminal matters, the Roman government apparatus just did whatever it wanted or what the emperor ordered, and this could change drastically from reign to reign. So, for example, Marcus Aurelius had much more moderate policies than some other emperors, but these were not laws; they were imperial policy.
The criminal authorities in Rome, called magistrates, could more or less do what they wanted. So, for example, if someone went around making speeches against the emperor, a magistrate could have him seized and beaten up or killed without any kind of trial. The magistrates sensed the will of the emperor, so when, for example, Marcus Aurelius made speeches about toleration, the magistrates would lighten up and not act against subversives as a result.