feasible? not by a long shot.

I had three students who were athletes when I was a TA. One was a hockey player the other two were track/field...

I don’t think it’s outside the realm of possibility, but it will require LOTS of dedication on your part. Of the three students only one had an issue with time management. 

If you're serious about it, dedicated and are willing to make sacrifices, sure why not. Work smarter, not harder and have plenty of sleep and you'll be fine.

It will be like having two wives.  One will be constantly unhappy.

I knew one volleyball player and one track guy. Neither were particularly great at the architecture thing, so I hope they were good at sports.

That said, they both were in the studio, doing their work.  All you need to do is manage your time.  Establish priorities.  All you need is a degree and decent enough work for a portfolio. Unless we're in a recession, you'll be able to find some sort of job. 

Is no one willing to address the bigger question here?

Is a career as a professional lacrosse player more lucrative than an architect?

Ask the school. It was not allowed at mine.

For sane people sports is the dream career.  

I was in marching band for the first 2 years I was in architecture school. (I'm from the south so this was a huge deal at my college.)  I quit because I didn't have the time to go to all of the rehearsals (1-1.5 hrs/day M-F, some Friday evening rehearsals, and at least one 2 hr sectional/week) and the games (all day Saturdays with some weekend away games) AND do all of my studio work.  I had friends that made it work for all 4 years though.  They were really good at managing time, but I was not.  Honestly, I got really tired of hearing people with much easier majors complain about how they had to write a paper or study for a test when I was barely making it through practice on very little sleep.  

So you can probably do it, but yeah, either your work or your sport will probably suffer. 

I did sports while in undergrad.  It was tough to manage, but for meets/travel - since it was mostly only on Saturdays - I'd do my non-studio coursework while in the bus/van, on the plane, or waiting for thing to start, and prioritized studio work on Sundays. There were some conflicts with class time and practice, but I made arraignments with the coach to either come late or do a morning workout on those days.

I did well in studio and in my classes, and was pretty good at athletics, but I regretted not doing more arch competitions, being involved in social groups like AIAS, or other things that would get my work noticed more while in undergrad.

I felt I was busy then, but it was nothing compared to working full time while in grad school with a baby at home.

Oh yeah, all the best students achieve greatness that way.