I have a set of 24 (over 48 ft) string lights that came with 1w led bulbs. I need more light, so I was wondering if I can replace the bulbs with 2w leds that produce more lumens.
Frame challenge: it is likely that a new string with brighter bulbs may cost less than replacing the bulbs in the existing string.
If the above is wrong, or you decide to replace the bulbs anyway:
Check the label or instructions that came with the lights (or web-search to find the instructions), to see if they have a maximum wattage allowed. Your present load of 24 x 1 watt bulbs is 24 watts. The new load of 2 watt bulbs would be 2 x 24 = 48 watts. If the label is more than 48 watts, then you should be OK, otherwise, no changes allowed.
Also check the power supply feeding the string, if there is one. The power supply would probably have a label on it showing its output. If the output is shown in watts, does the new 48 watt load overpower or come close to the watts on the power supply? If yes, then don't do the change: A 75 or greater watt power supply should be able to handle 24 or 48 watts of load. A 50 watt power supply will be close to or at maximum load and may burn out soon. Less than 50 watts will not feed the load and will burn out quickly. Burning out the power supply is a bad idea. Also match the voltage on each light to the old light voltage. 24V lights on a 12V light string won't work, nor vice versa.
If the output of the power supply is in "volt-amps" (something like this: "40VA"), consider this number as the watts (=40 watts).
If the output of the power supply is in a number of volts at a number of amps (something like this: "12V 3A") multiply volts and amps to get watts (12 x 3 = 36 watts).
If the string is plug-in, with no power supply, and the label allows more than 48 watts, go for it.
If the string is plug-in and you cannot find a maximum wattage shown anywhere, the safe thing would be to buy a different brighter string.