So, for full disclosure...and I get that this makes the whole thing confusing...yes, in DC (and Marvel) a character has to at least equal or exceed light speed to time travel. And Jay has time traveled after hitting superluminal velocity in JSA 20. But as mentioned, that was after he stole Black Adam's speed to hit the light speed barrier. He was otherwise incapable of doing that on his own at the time.
In the instance of the speedsters who could not follow Wally through the time stream in
Chain Lightning, those speedsters specifically could not follow Wally through time because none of them were faster than light, or could even equal light speed at the time.
Classic Jay was faster than light.
Attachment 98159
But as he clearly later said in JSA (and I believe DK touched on this already, so if so...apologies), Jay wasn't light speed in JSA.
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To be clear then, the treadmill not only helps for precise time travel (it was hit and miss for pre Crisis Barry Allan...sometimes he needed, sometimes he didn't, but he was routinely faster than light, which also muddies the waters), it also provides a vehicle for time travel for folks who cannot travel faster than light in the first place. Clearly, that was the case in
Chain Lightning. But a blanket statement of, "the cosmic treadmill only works for people who are faster than light already", is completely untrue.
At least all the way up to
Final Crisis.