I have got 4 years old Sony Vaio laptop, I3, 6gb ram, 320gb hdd.
Originally laptop came with 2gb ram, I upgraded and added 4gb more to it. Installed original Window 8.
I am able to process RAW files using lightoom with decent performance, exported around 100 processed raw files, took a little while but never crashed.
So basically the idea is that get a decent configuration laptop in your budget range and then add more RAM to it to help performance somewhat, you should be able to get decent performance out of Lightroom and photoshop. Only other alternative ofcourse is to increase budget and atleast I5 with min 4GB ram.