Proper BMS seems overkill for low power LED...why not just sense voltage of each cell, and stop the charging when either cell goes overvoltage?
AND...stop the discharging when either cell goes undervoltage.
That is a kind of BMS though, i suppose.
You could put in active cell voltage balancing, so you can squeeze the most power in and out of the cells...but it seems overkill for your application.