If you're riding a Peloton or using spin studio bikes, yes—you need LOOK Delta compatibility. These bikes come with LOOK Delta pedals, so your shoes must be able to mount Delta cleats.
The tricky part is that LOOK Delta and LOOK Keo share the same 3-bolt drill pattern on the shoe sole, but the cleat shapes are completely different and not interchangeable. A LOOK Keo cleat won't clip into a Delta pedal, and vice versa. This is a common mix-up that can leave you unable to clip in on ride day.
The good news: any 3-bolt road shoe will physically accept a LOOK Delta cleat on the sole. Just make sure you purchase the correct Delta cleats separately if they aren't included with your shoes or pedals, and you'll be all set for your spin sessions.