I guess the question is not so much, do I need a current limiting resistor, as do I need a voltage dropping resistor.

Pin 1 of this IC will sink 5mA when the charge voltage fall between .6V and .35V, at which point aprox. 5mA is sinked through D1(LED) and R1(Resistor).

Not really sure what I need, an LED that lights up well enough at 5mA?
Will an LED rated at 3V/20mA light up with a 400 ohm resistor in series and only 5mA passing through it?

datasheets-LTC4054L-4.2

 

You missed a chart. Bottom left of page 4. The charge pin will dump over 20 ma to ground. Keep reading the specsheet.

 

Oops! So Pin 1 is a Charge Indicator and not a Charge Complete indicator.
Actually, both. When LED is lit, the battery is charging, When the Battery is charged, the
LED should not be lit with only 5mA. Thus a 400 - 500 ohm resistor ought to work fine...