To make things more readable, I'd like to put a little more margin between lines of text. I couldn't find an answer with
man terminator_config or any of the Preferences panes.
Terminator doesn't support this. In fact, Terminator, such as many other terminal emulators (e.g. gnome-terminal, xfce4-terminal, mate-terminal, roxterm, sakura, tilda...) uses the VTE widget for terminal emulation and the VTE widget does not support this.
You might want to take a look at how fonts are defined, and whether you can take an existing font and create a new one by adding some more space at the top and bottom. I don't know how to do this.
You might also want to take a look at fontconfig, the library responsible for locating the desired font. It might have such a feature, I don't know.
Or you can easily build a modified VTE for yourself, see https://bugzilla.gnome.org/show_bug.cgi?id=738781. Make sure to first find out the exact version of VTE your Terminator is using, which in case of Terminator version <= 1.0 will probably be vte-0.28.2 and start off from that version (or upgrade to Terminator 1.90 and go for vte-0.fourty-whatever).
VTE implemented this feature in version 0.52. This makes super easy for Terminator (or any other VTE-based terminal emulator) to add support for this. If you still care, please file a feature request against Terminator.