I want to be clear that not any of this is easy.
I think as soon as you try it, your first attempts are going to be very blurry, squint inducing, and especially very dark. A lightfield display, in order to achieve the same level of perceived brightness as a traditional 2D display, needs to generate 2-10 times (perhaps much more) more actual light, with all the requisite power requirements that entails, since the light is distributed directionally instead of diffusely.
Going in this direction basically takes the level of resolution and precision in image reproduction we've achieved back a decade or 5, since the "pixels" or resolution units are spread over many more views than just 1 or 2, or perhaps something more recognisable as a continuum of "infinite" views, or whatever number is visually indistinguishable from infinity.
Why would it need to generate more light? Suppose you told your lightfield display to simply display all white - wouldn't its light distribution be the same as a white LCD, hence taking the same amount of power?
In a projector system you generate light, and then you block it using either photographic film or LCD to produce the image. A lightfield display can be thought of as a 2D, higher resolution generalisation of a lenticular ("no glasses") display, or for example, the display of the 3DS.
In these kinds of displays, you have a light generator (LED or flouro or reflection) with the same surface area as a normal print or display. But to produce the directional light, for say the left eye, you must block the portions of the image that relate to the right eye from the light travelling to the left eye. And vice versa. This halves the amount of light for 2 directional images. thirds it if you want 3. So you end up with an image that is much darker then normal. you must compensate by generating 2 or 3 times the amount of light.
This problem gets worse the more "views" you add on. So if you want 10 omni directional views you have to generate enough light for all of them, since, even if you set everything to "white", as you suggest, most of that white is getting blocked from your view.
Or to put another way, you get allocated a smaller source 2d image plane surface area to generate your viewpoint.
Why do you have to block the light? Sure, primitive stereo parallax barriers like the Nintendo DS has do, but nobody uses parallax barrier tech for any proper lightfield application. The system you mentioned, a lens array over a high-PPI screen, blocks nothing; light is only refracted. Ergo, the energy required to run the screen is the same as without the lens array, e.g. a normal screen.
Going in this direction basically takes the level of resolution and precision in image reproduction we've achieved back a decade or 5, since the "pixels" or resolution units are spread over many more views than just 1 or 2, or perhaps something more recognisable as a continuum of "infinite" views, or whatever number is visually indistinguishable from infinity.