I don't think so. Maybe Tramp was born without a home. You never know. It is unknown. But, by the way they first meet, I doubt that they new eacthother before they meet in Lady's front yard. It must have been a rumour, because I've never heard this before. This is a very interesting question, but I'm still sticking with my original answer. I dobut that they met before the occasion in the front yard.

I have searched around for sometime and have found no concrete evidence that validates this claim. Disney has had no pressure or interest at the moment to even make a back story about the origins of Lady or Tramp. Therefore, wherever you read it might possibly have been a fanfic and not the actual story before LATT1's plot.