How Long Does It Take To Learn To Play The Piano With Lessons?

It's different for each individual.  It's easier for some than it is for others.  It can depend on the teacher, how much one practices, how well a person can read music, and some are more musically inclined than others.  A lot of factors can enter into it, so it's really impossible to tell how long it takes.

One of the piano teachers who regularly posts on the Piano World forums suggested that it takes 1500 hours to "sound like a piano player".  I believe that is about right.  That's 90 minutes a day for three years.  If you could practice for 45 minutes in the morning and 45 minutes later in the day, that would be ideal.  If you can't do that much, don't worry about it, it will just take you longer to get to the same level.  Enjoy the journey, it's a worthwhile thing to do.

PS:  When you are first starting out, you'll probably only want to put in a half hour a day, as you'll get fatigued.  As your dexterity improves, you can start increasing your practice time.  After a while, your biggest regret will probably be that you won't have as much time at the piano each day as you would like.