We were doing the Taylor in hardshells and IKs at 150 on the Almont gauge and 79 on the Dam gauge earlier this year. Its not clean but you'll be surprised how well it goes. Like Logan said, it should be more than good to go until at least Aug 1.
[TR] Upper Taylor ELF
This is a trip report from early may at ELF flows, with even less water but still fun.
The lowest I've heard people doing the LF Box is 150, but I would have to say closer to 200 is better. Its a wide riverbed, and the other thing to consider is that it is 11 miles with no access besides the put in and the takeout. It looks like its next to a road but that is decieving, the river is actually tucked in a flat bottom but vertical walled box, with the river located a good 100 vertical feet above it. Hence the name, "Box". Go to the Taylor and lqp it a bunch of times. Its the better of the two at these flows anyway.