What do you mean to indicate by lighting a LED with "low battery mode" and seemingly different, "low battery indicator"?
These indications seemingly relate to the battery while in use in a circuit, rather than in its charging, and so are not the responsibility of a charger IC.
Adding these features to a charger IC can easily be accomplished with a cheap 8-pin MCU with an internal reference for its internal A/D and use only micropower, yet wake itself up periodically to make an accurate check of the battery voltage and indicate it with a LED. Additionally, the LED can indicate a fully charged or low-battery condition and your circuit running in low-power mode with different LED modes of being on, off or blinking in one or more patterns. With a MCU a single LED can serially display the actual battery voltage in a parsed series of numbered blinks, perhaps periodically or by pressing a multi-purposed switch for a certain length of time, and the same MCU can also be used to create a step-down converter to charge the battery as well, eliminating the charger IC.
Also, depending on the battery voltage and acceptable accuracy and your visually acceptable precision of indicating a low-battery voltage state, and in consideration of your current use requirements, a circuit can be created with maybe two transistors two LED's and about 3 to 4 resistors.
Of course there are dedicated IC's aplenty to do this job as well.
If the voltage is >2V then a single LED or LED + PNP transistor and a LED's brightness can indicate a low-battery condition. A high-efficiency LED can give a bright indication with <1mA of current use. Using two transistors and high-valued resistors, a low-battery threshold can light a LED and further save battery use and only light the LED when the battery is low.
If you are adverse to the complexity of getting a MCU to do this job, you can also use a CMOS 555 timer and get it to slowly blink a LED by using a single PNP transistor to keep the 555 timer in a 60uA low-current state until a low-voltage threshold of the battery is detected..takes just one more transistor and a resistor or two.