Look up with LM358, output are bipolar and output can not be lower than about 1 volt over GND.
Page 4 of the PDF above says that the output can go down to 5mV typical, 20mV max. But that doesn't really matter, we aren't asking the output to go that low.
The inputs are rated to go down to the negative rail, ground in the case of a single supply.
Both inputs and outputs can't go within about 1.5V of the positive rail.
In any case, simpler to use a purpose-built constant current switch mode LED driver, unless you have the other parts and can't easily get such an IC.