I have been installing sound and video into church sanctuaries over the last few years. As stated in previous posts, getting a church community to accept a new method of advanced worship can be a interesting and stirring time. One point I believe is that, if the Good Lord did not want us to worship with new methods of learning, we would still be using stone tablets.
Recently, I did a job in a retirement community west of Phoenix which has a very conservative and seasoned membership. They held an all-member vote to ensure that the decision was going to be well accepted. It was passed (I was told) by more than 2/3 of the membership. We located a new control booth in the rear of the sanctuary toward one side. An audio snake was installed to feed the existing lines to a new mixer in the booth area and provide the return signal for the amplifiers. We also provided Ethernet and control cables for the two Sharp 80 inch screens, located one to the left and one to the right of the chancel area. This is good, as in many sanctuaries, having a drop down screen in front center is simply not a good idea as it will cover up much of the beauty of the chancel area. These screens can also work even in direct sunlight, in fact the sun was shining directly on the 80 inch Sharp LED monitor and the viewable picture was still very good.
Try this with a projector and you will not even be able to see any image, regardless of the lumens. Lumens are very misleading. People many times think that lumens can compensate for a bright or sunlit environment, but high lumens cannot.
Projectors can only be used in locations where the chancel is dark and is not a creation of beauty (think mega church). Not a slam against mega churches but many are re-purposed big box retail space, not old world, grand architecture.