Theater on the Lake is owned by Chicago Park District, and you can view their schedule at www.chicagoparkdistrict.com. Their website directions tell you how to get there by bicycle, and I saw plenty people arriving by bike. After all, if you're going to Chicago to enjoy the lakeside, stay on the shore in the evening and you don't have to miss the theater scene. You don't have to dress up, either - shorts, even lycra, acceptable.
We saw a Lillian Hellman play, "Another Part of the Forest," performed by the Eclipse Theater Company. The play was wonderfully acted and staged and the theater small enough to make the performance even more special.
One drawback was the temperature. Perhaps the theater is air-conditioned. I'm not sure. There are ceiling fans, but the little hand-held plastic fans all guests were given at the door were kept busy all night, a few hundred of them going at once. This may have been appropriate for a Southern family drama, but it was distracting. I still enjoyed the play and will return to the Theater on the Lake, since they do such literary masterpieces as "The Cherry Orchard" (the week after I was there, darned, for it's my favorite).
To get to the theater, you must take the CTA red line to the Fullerton Avenue stop, then walk east all the way to the Theater, just a mile (their directions insist), maybe a mile and a half. We enjoyed the walk out Fullerton and back to the CTA because it is a pleasant neighborhood of brick & brownstone walk-ups with well-planted little yards, intriguing architecture, and plenty of people out and about, walking dogs and visiting. We felt like we lived there.