Generally speaking, this request does not sound like a good idea. Laptops can be a significant cost for a student. Some may not have a laptop. Some may have a device that they already use for portable computing needs, but which is unsuitable for development (like a tablet). These people will then be forced to purchase a laptop just for your class - students already balk at paying $100-200 for "required" textbooks, how do you think $1000 for a laptop will go over?
The exception is if your school provides laptops to the students. But consider that cost is not the only factor. When I started college, I was very excited that I could finally bring my laptop to class and take notes more effectively, as we were not allowed to use devices in high school. After two days of carrying the heavy laptop around campus, my back was in excruciating pain. I never brought a laptop to school ever again unless I really had to. Keep in mind that I am healthy and have a strong back - what about students who have injury or chronic back pain and cannot carry heavy bags at all?
You could of course demand laptops regardless, and I doubt there would be repercussions even if it is unreasonable. But it is virtually guaranteed that with 90 people, you will have some sort of issue like those I describe above, it will not be as simple as asking everyone to bring one.
By way of suggesting a solution, I think Option 1 sounds great. You have astutely stated the key advantages. I will add that some lecture halls have small tables which make working with a laptop clumsy and unergonomic. Also, not only do students have to set up the software, it has to be compatible with their system - by using lab computers you get around this problem.
Your main objection to this appears to be the projector screen. First of all, most students will see it to begin with. For those who can't see and can't sit at a better location, you can distribute a PDF of your slides. You can also distribute paper handouts. If you are worried about paper wastage, you can print only a few copies for those who ask for them. If you print them one sided students can also recycle the handouts and use the back as scratch paper or for note taking.
If you decide to do Option 2, you should modify your policy and say laptops are strongly encouraged but not required, and explain why you believe having the laptop is helpful. However your lecture should be designed such that it is possible for anyone to follow without a laptop. If the demonstrations are essential, it should be possible for the student to take notes and then do the demonstrations at home.
Most of your students will probably be able and willing to bring the laptop. The rest can take notes and follow up in their own time at home or a library computer.
Another suggestion since you intend to teach R: Rstudio has a Server version, where the R code lives on a central machine and users interact with it through a webpage. This way users need only a JS-capable browser, no installation necessary. The web interface looks very similar to Rstudio, so when the students are done with the class they can figure out how to get R set up on their machine, and practically all that they learned in your class from the webapp will transfer.