LP311 collector remains at ~11V when "low"
You are trying to draw too much current from the output. If your supply is 12V then the current would be 60 or 70mA, which is far higher than the low power comparator can supply. If your supply is higher, it's even worse. 

You say: 


  However, increasing the load current and therefore increasing the comparator input difference should then bring collector voltage lower, but this was not the case.


But this is not true, the output current will be limited by the available base current (which has more to do with the internal biasing networks), which will not increase for differential inputs beyond a few mV. With a 5V supply (4.5V in the specifications) it is only guaranteed to sink 1.6mA with a defined maximum \$\text V_{OL}\$. 



So add a buffer for the LED and all should be well.