OK
I'm willing to believe that there is a mortice lock (unusual)
You will have to take the hinges off
Wedge some timbers or bricks or something under the gate first so it does not fall on you.
It will not be too heavy for a man to lift, but I don't know how strong you are.
When you have removed the gate, lie it down on its hinge side (lock edge facing up) and photograph the lock. There will probably be two screws. If you undo them you can pull on the bolt of the lock and it will pull out of the door. If you then photograph the lock from all sides, with a ruler in the pic, we can suggest a lock that might fit.
You can put one or two bolts on until you get a new lock (or the old key turns up). Ne'erdowells often kick a gate by a road to see if it comes open, so shed bolts, not bathroom bolts.
Is there a DIY shed, hardware store, Wickes, Screwfix or Wilkinsons near you? Have you got some screws and a drill?
You will need a set of screwdrivers in good condition, not worn out, as the screws may be rusty and need a good fit.
If you take the gate off today, have you got someone to help you lift it up and refit it?