What does "class 2 input only" mean in my LED desk lamp?

You're correct that "input" means the power source. "Class 2" and "Class II" are different, however. The former refers to wire size and other specifications, and the latter refers to the insulation (shock protection) standard of the device.

More on that

You need to find the power supply that has the correct voltage and wattage. For example the Output will usually be limited and the wattage specified as 25-30 volts at 9 watts is one I have. They are usually double insulated and power limited (considered safe not a fire hazard).

Look on the “brick” or plastic block. It will have the voltage and wattage stamped into it. Led drivers usually have a range of voltage at a specific wattage. Power supplies for computers have a specific voltage and the maximum current they can supply.