I am a lefty who learned a right-handed serve in less than 2 week. However, I already had an advantage in that I throw better with my right arm than my left. My lefty serve is still much better and feels more natural than my righty serve. This is an indication that the mechanics for throwing a ball and serving with a racket, while similar actions, are sufficiently different.
If you are serious about learning a lefty serve, try throwing an old racket in the park. Not a bad idea to learn to throw a ball first. When throwing, try launch a launch angle close to 45 degrees. Once you've mastered that, throw at a launch angle of 75 degrees or more. When you start to feel comfortable throwing a ball, get out an old racket or two and start throwing those. Try the same launch angles I suggested for ball throwing. The steeper launch angle should help you achieve a decent racket head drop (with the 45 degree throw, probably will not).
When performing the racket throwing, try it with an abbreviated preparation or just start in the trophy position. When first attempting to serve left-handed, start off in either the racket head drop "scratch" position or the trophy position at first. If you are not getting a decent racket head drop when stating in the trophy position, the start off in the "scratch" position for a while.
Some players stick with simplified motion for a week or several weeks or more before moving on to the next stage of the progression (i.e., trophy pose serving). If the conti grip is too awkward at 1st, try a semi-conti grip for a while. I would NOTstart of with a FH grip tho'.