XL6009 min input voltage is 5V (see datasheet). Not only it will not supply necessary current, but when voltage of liion goes below 3v XL6009 fails to regulate properly and voltage spikes on output. Observed this behaviour on two units. Summary is that XL6009 is not suitable to boost liion bateries. What I recently used on few projects to boost liion voltage is cheap "power bank" circuits. By default those boots liiov voltage to 5v. I modified feedback voltage divider to increase this voltage to my needs. Don't forget to remove USB output if you do that! You do not want to burn USB device with overvoltage by mistake.
