The OS you are running should have a Scale Factor setting where you can Scale Up, 200%, 300%, for this purpose. But the newer versions of LR and 99% of all newer program kind of do this on there own or have a preference setting to do it. LR 3 came out 7+ years ago before there were high resolution monitors.
Go to Preferences > Interface, and see what options you have for font size (It's a long time since I used LR3).
I tried changing the size in the interface but it didn't do anything. I'm worried that LR3 just isn't going to work with the high res screen