Well...it's not that simple. First of all, although Wonder Woman first appeared in All-Star Comics #8 (1941), she didn't get the lasso until Sensation Comics #6 (1942). And the lasso - then called the magic lasso - didn't compel people to tell the truth. It actually forced people to do whatever Wonder Woman wanted, and sometimes that happened to be answering her honestly. So you see, the lasso has more to do with his night life than his day job.
In the Wonder Woman tv series (1975-1979), however, perhaps because of standards at the time, Wonder Woman only used it to make people tell the truth. So it follows that after Crisis on Infinite Earths, the lasso would be reintroduced as the Lasso of Truth in Wonder Woman #2 (1987), which it's been called ever since.