I can hardly remember an old TTL gate high output current but I think it can drive a few mA and still be above 3V.
The datasheet for a CD4011 Cmos Nand gate with a 5V supply shows that it can typically supply 4ma to a dead short to ground and will be at 2.2V with a load current of only 3.5mA. A very dim LED. A current-limiting resistor won't make any difference and is not needed.
Its output current is typically 10mA to 20mA with a 10V supply, but its voltage might not be high enough to produce a logic high.