TomTop offers this Mini Portable LED LCD Projector in Black for $42.99 with free shipping. That's the lowest price we could find by $8. It features a 480x320 native resolution with support for up to 1080p, 500:1 contrast ratio, 20" to 100" projection size, remote, SD card slot, USB, and HDMI and VGA inputs.
Note: The specs for this item mention both 120- and 200-lumens brightness. It's unclear which is correct, and some sellers list the brightness on this projector as 60 lumens.