I don't think you even have to say that you have competing offer $1.25X.
Simply stating you have a competing offer also for $X is completely believable and will probably get you a improved offer from one of the two interviewing teams.
Even if it doesn't and you accept at $X then at the very least your new employer now knows that you liked them best. Which is not a bad way to start a new job.
Either way I would never lie and say I had an offer when I didn't. Lying in general is a bad faith strategy and will often come back on you at some point.
Simply stating you have a competing offer also for $X is completely believable and will probably get you a improved offer from one of the two interviewing teams.
Even if it doesn't and you accept at $X then at the very least your new employer now knows that you liked them best. Which is not a bad way to start a new job.
Either way I would never lie and say I had an offer when I didn't. Lying in general is a bad faith strategy and will often come back on you at some point.