I had problems running an early version of LW on OS 8.5 So I would guess you'll have similar problems.

I hope Java came with your operating system. I can't remember if Java was included with OS 7. I don't recall it being included. You might have problems obtaining Java which you will need in order to run LW. See these articles & check the minimum installation requirements http://docs.info.apple.com/article.html?artnum=22133
http://docs.info.apple.com/article.html?artnum=28027
http://docs.info.apple.com/article.html?artnum=75097

So I can't give you a definitive answer. I'd tend to say OS 8 would probably be the minimum now.