I'm afraid that the article that Akash refers you to is based on working with Lightroom on a computer, exactly what you did not want to do.
You can't transfer presets themselves between phones, but you can export the settings of a preset as follows. Select a raw photo and apply the preset to it. Do not make any other edits. Now export this photo as DNG. Use AirDrop or something else to send the DNG to the other iPhone. On the other iPhone, import the DNG into Lightroom Mobile. If everything worked correctly, then you should see the edits coming in too. Save the edits as a new preset and you're done.
P.S. This is assuming that you do not have an Adobe Creative Cloud account and work with the free version of Lightroom Mobile. If you have an account, then logging into the same account on both phones is all you need to do. Everything will be synced automatically.
-- Johan W. Elzenga