What lightweight Linux distribution would work well on a 2 GB RAM netbook?

Some people have managed to run Raspberry Pi operating systems on older non-Pi computers, but compatibility depends heavily on the hardware and image. A normal x86 Linux distribution is generally a safer route and will give you better support for the netbook's processor and peripherals.

Lubuntu, Xubuntu, or Linux Mint with Xfce are easier, more complete choices that should still be reasonably light on 2 GB of RAM. A clean installation of 32-bit Q4OS may also be worth trying if the processor supports it, since Q4OS is already designed to run on older hardware.

antiX, Tiny Core, Puppy Linux, and Alpine are worth looking at if you want the smallest possible system. For a distraction-free writing machine, Tiny Core or antiX could be enough, though they may require more setup than a mainstream distribution.

The storage device may be the biggest bottleneck. Replacing an old hard drive with an inexpensive SSD can make the whole system feel much faster. I would also do a clean installation, remove the old Windows partitions if you do not need them, and let the installer create swap space. For Dropbox, the web interface is probably lighter and simpler than installing a synchronization client.

Raspberry Pi OS is primarily built for ARM processors, while most old netbooks use x86 hardware, so it usually is not the right choice. Regular Debian can work very well on older machines if you install a lightweight desktop environment or window manager instead of a heavy one.