If an "information" charging you with public lewdness was filed prior to the running of the statute of limitations, then yes you may still be subject to arrest and prosecution.
I would not expect to see a warrant for this offense to appear on a City warrant list, as this offense is a Class A misdemeanor and would not be prosecuted in the Dallas Municipal Court. The database it appears that you are referring to is for warrants associated with the prosecution of Class C offenses in the Dallas Municipal Court.
A Dallas bonding company and/or the Dallas County Sheriff should be able to tell you if a warrrant for your arrest still exists for this case.
I agree that if the State filed an information against you, it tolled the statute of limitations while it is pending therefore the State can still try to proceed. (There may be speedy trial issues & other issues about you availablity, etc. For example, if you have updated your driver's license in Texas, they should have arrested you but failed to do so, etc. You should talk to a lawyer about this.)
Call a bail bondsman. They can check the county records with ease to determine if there is a warrant. You can make a non-arrest bond by putting up the full amount or hiring a bondsman. You would then just walk through - they would take your photograph and fingerprints.
I would hire a lawyer & face the situation before you end up arrested in a situation that may be embarassing and very, very inconvenient. It is also better for you in dealing with the case.
There are LOTS of great lawyers in Dallas, and many of the firms have associates if you want to spend less money.