Filing the appeal does NOT stop the lockout by itself. To stop the lockout pending appeal, you have to first ask the judge who ruled against you, and if he refuses, then you ask the appeals court to do it, and they might. Because the trial judge rarely grants the motion to stay pending appeal, this service is charged as the double drafting for the two separate motions.
The first part is a simple petition for stay, submitted to the same judge that ruled against you. Usually, that is denied. The next step is to file the Petition for Writ of Supersedeas with the Appellate Court, asking them to stop the lockout pending appeal. It requires a voluminous record of what happened at trial, Bates Stamped pages and an emergency stay request. That is where most of the time is spent. If successful, it is cheaper than moving.
Keep in mind that the required condition of the stay pending appeal is that the monthly rent be paid on time to the court or to the landlord. You are not staying for free pending appeal. You just avoid having to move out.