Unfortunately, there is no way for printer to know how many labels left in the roll, because the label roll could be for whatever size of labels, such as 4"x6", 2"x3", etc. The label roll is just a dumb roll of labels, unlike cartridge, which could have a smart chip to count the labels and the remainders.
But you can come up with some kind of algorithm in conjunction with the printer's odometer reading and the stock of the label rolls you have. If you know how many labels per roll, for example, you can read the odometer when the label is installed and poll the odometer along the way to see how many labels have been printed. So that, you can roughly know how many labels left on the roll.