Lightroom 3 tiny interface text etc

What is the screen resolution?

From the screen shot I’m guessing that it’s rather high, and that the rest of Windows and current applications are probably running on that monitor in HiDPI mode. HiDPI = 2x pixel density, so on a 4K display (3840 x 2160), HiDPI compliant applications run at 1920 x 1080 at 2x pixel density. But applications that aren’t HiDPI compatible will run at 3840 x 2160 at 1x density, making the interface look tiny.

Without knowing the screen resolution, this is my guess:

Lightroom (Classic) 3 was released in 2012, just when HiDPI displays were being introduced so I doubt it knows how to scale for HiDPI. It may be running at 3840 x 2160 @1x. If this is the case, the Lightroom UI scaling settings won’t help you because they are just refinements on top of the general OS display resolution settings.

I don’t know when HiDPI compatibility was added to the orignal Lightroom (what is now Lightroom Classic), but certainly the current version is fully compatible and the UI won’t be tiny.

I actually use a Mac (where HiDPI is called Retina), so I’m a little fuzzy on if there are any Windows settings that might fix this for you. I know that Windows allows interface scaling across the entire OS, but I forget if that can be applied on a per-application basis because if so, that would be one way to solve it. By "interface scaling" I don't mean whether a display is set to 3840 x 2160 or 1920 x 1080, I mean a separate option in the Display settings for Windows that lets you scale the UI 125% or 150%.

In more recent versions of LR on Windows:

The font size of LR's main menu bar and some standard dialogs is controlled by the Windows Settings > Display > Custom Scaling.

The font size of the rest of LR is controlled by LR's Preferences > Interface > Font Size, which you can set to Small, Medium, Large - 150%, Larger - 200%, and Largest - 250%.

I'm not sure if LR 3 has those larger sizes, though.