The MAX96706 datasheet* states in its EC table, page 8, that the test condition for a logic low on the open-drain outputs is 3mA. This applies to ERRB, LOCK, and LFLTB. So, you can safely sink up to 3mA to those pins. 3mA should be enough to drive an LED with moderate brightness, but a gate or a FET is recommended for more current to drive a brighter LED.
* MAX96706 datasheet revision 2 (Nov. 2018)