Can I install pokemon lab on my thumbdrive/external hard disk
 

Topic. And does it work if I use it on another pc (assuming it has java and all)?

I'd actually really like to know the answer to this question. I haven't been able to dl it to a flash drive and use it, but that may be because I don't know much about computers and stuff.

You can. You need a custom jnlp launch file, and all the jars. Just place them in a folder and execute the jar file. You WILL need java on the other computer. It won't work if that computers java his issues itself.