Passing <5V through bus of tri-state transceiver
It is not entirely clear what you are asking here, or what you say happens.  Sometimes things outside the limits of the data sheet will work - or at least seem to for a while.

The output voltage of your 74LS173 is so low because you are heavily loading it with the LEDs, and because LS logic doesn't have all that strong output drive to begin with.  The best solution would be to use a CMOS inverter to drive the LED cathodes instead of the anodes, and to isolate driving them from other consumers of the logic signals being displayed.  But you could substantially improve the situation without changing the topology by using a 74HC173 or 74HCT173 which will drive much closer to the rail even when loaded, and/or by enlarging the LED resistors so they draw less current.

With regard to the 74xx245, if you use specifically 74HCT245 (note the "T") that has an input high threshold of 2 volts or less, even when powered at 5v.  As such, it has a good chance of helping you by doing what all digital logic is designed to: restore the "noise margins" by taking any acceptable input, and turning it into a definitive output as close to the rail as its output structure can accomplish against a given load.