Your post suggests two different kinds of lag tests -- so I'll address both separately...For testing the lag difference of two displays
(A) SMTT can do this.
(B) There's an upcoming TestUFO motion test coming soon that will let you do SMTT-style lag testing via a TestUFO pattern. (It may take a few weeks to a few months before it becomes publicly available). You'll still need a camera (photographic or video).
(C) High speed camera can do this (to an extent). Film both displays running simultaneously. Determine how many frames behind the second display is from the first display. Multiply by 1/240sec for 240fps camera, or 1/1000sec for 1000fps camera. There's your lag differential. Also, lag differentials remain the same whether you are streaming or not, so you may want to do http://www.testufo.com/flicker
(full screen -- warning, it'll hurt your eyes) because it automatically displays frame numbers, and also makes LCD scanout easier to see in high speed videos. If one display is scanning half-a-frame behind, you can tell that particular display is half-a-frame latency. Make sure the two displays are side by side -- if one display is bigger than other, move it further back until it's approximately the same area coverage in the image (displays same height in photo or video).For game button-to-pixels lag testing
The best way to lag test buttons-to-pixels is the high speed camera
(slo-mo). Basically how fast you see response from your controller. Even iPhone/Android 240fps is usable.
A modified mouse helps a lot, if you need higher accuracy + 1000fps. This testing technique was invented by Blur Busters for G-SYNC lag testing in GSYNC Preview #2
A 480fps camera can do lag testing with ~2ms accuracy, and a 1000fps camera can do lag testing with ~1ms accuracy.
The modified mouse helps signal button press, but it's also possible to do it via an unmodified the high speed finger press (and use button contact in high speed video). This would provide ~2-3ms accuracy.
If 240fps is not enough (4ms error), cheap low-resolution 1000fps (1ms error) can be had with a few cameras purchased from ebay (Casio EX-FC200S, EX-ZR200, etc) and a bunch of other brands.
iPhone 240fps can be suitable for lag testing if you are willing to tolerate a ~4ms inaccuracy. At only 240fps, you can just simply do the fast finger press (hold mouse with one hand, begin filming, then zoom down your other finger from several inches above, straight downards as fast as possible onto the mouse button on a raise mousepad platform saitting directly in front of the screen. (while the high speed video is filming) Playback the slo-mo and find frame when the finger contacts & the frame when the screen reacts (e.g. muzzle flash, movement, begin of jump, etc). Count the frames in between. Multiply by 1/240sec. And you've got your button-to-pixels input lag (rounded off to nearest 4ms). Do maybe 10 passes. (You can do it all on one 240fps filming). Use a player that has easy frame advancing (back/forward) and frame number counting.
For streaming latency testing (50-100ms lag), you can easily get away with smartphone highspeed video (240fps) and an unmodified mouse (high speed finger press).