Maybe lite version will run, but not very well if you want to browse (which easily eta a GB for itself). You might want to look at some very light Linux system to run more smoothly. Try MXLinux.
Keep in mind that it is one thing to run the OS itself, but then you have to add whatever programs you want to run on top of it. Web browsers in particular want to use as much RAM as possible, and as the web becomes more "modern", the more work they have to do. LibreOffice, or equivalent office suites, can also be relatively RAM hungry.
My advice is to keep as few programs as needed running at the same time, and when browsing online, keep the number of tabs to a minimum.
If you have the chance, consider upgrading your drive to an SSD if you can, which is another bottleneck for performance.
And lastly, since this is an old computer, it might actually come in handy to open it up and clean its insides from accumulated dust and re-apply thermal paste to the CPU. See if there are any videos online about this for your particular laptop model, but any video will do to give you an idea on how to do this.
You could try a Distro from I heard a While ago. It is intended to use on USB Sticks but it could be good for Your low Spec Machine, too. It is Mini OS:
With your computers SPECS, I really don't see it running anything above Zorin OS zorin os 12.4 lite 32 bit, as it only requires a 1GHZ CPU & 2GB of RAM. However, when needing to run APPS as well, its more then likely, you'd have to run on Zorin OS 9 Lite, which requires 1GHZ CPU & 1GB RAM.
Both of those operating systems are long outdated, and no longer supported. Which means, security matters when connected to the net. If your machine is really that old, I think its time to buy a modern computer.
You can find legacy versions of Zorin OS at the link bellow...
