You've already gotten the answer to your questions (ticket must be purchased before travel, but it's good on any train that day, so no problem taking a later train from Interlaken Ost to Lauterbrunnen).
However, there's a reason the computer-generated itinerary shows such a short time for transfer at Interlaken Ost. It's very easy and doesn't take long. Unless you have a mobility impairment, or stop to use the bathroom, buy something, etc, you should not have difficultly making their suggested trains. Of course, if you do want to stop at the Coop, feel free to do so, as the trains from Interlaken Ost to Lauterbrunnen run every half hour.
I know that before you've been there, the process of getting from Luzern to Muerren seems complicated. Once you get there, you'll see it's easy. I'll just add my tip that doesn't often get mentioned: at the Muerren station, you don't have to climb stairs if you don't want to. When you get off the train, instead of heading up the stairs, head the other way (back the way the train came) and go outside. You'll see a ramp up to town.