If you've got an ies photometric file on the
fixture and
CAD of the room you can use software to do it. This also helps determine the best
layout for the fixtures. Rule of thumb, wall to 1st
fixture on either side should be roughly 50% of the difference between fixtures.
Some of the manufacturers have tools on their sites to do simple layouts, too. I know Cooper used to have one that would let you choose a
fixture, put in basic room dimensions & give it some performance specs & it would output a number of fixtures and a
layout.
Re: COU, if you can't get it from the manufacturer you can find another
fixture with similar beam spread & distribution (not always easy, but it can be done) and use the COU from its datasheet. If it's just not available I'd say you should calculate using at least 150% the number of fixtures that your initial
lumen calculation suggested. It's fairly rare to get a COU over 90% (though the fact that it's a
theatre means it's probably fairly high as our spaces tend to have lots of floor area & relatively little height, plus your LEDs are going to dim over time to about 70% at 50,000 hours (that's probably a long time, but even so, I'd use a maximum of 85%), and you'll see some dirt depreciation (even if you're cleaning these fixtures quarterly you can probably say you get a value around 95%. These relatively rosy calculations give me about 70% of the rated lumens getting to the floor, or a requirement of 1.38 fixtures to give you the rated lumens of 1
fixture. That's a relatively optimistic calculation, too.