I was also recently thinking of starting a LN node. Now I am worried: if I download the blockchain, would that in effect mean that my hard drive would contain content that could get me in trouble?
Chances of someone checking your hard drive for content is very low, but you can protect yourself with running bitcoin node with Tor, and having your hard drive encrypted by default (that can easily be done with Linux OS).
I wouldn't worry so much about that because running a node is not illegal anywhere, but it's always good to be ready to protect all files on your computer, not just bitcoin related.
Minimum you can do is adding strong login password and use separate device for node, not your everyday computer.