Apparently, that is not possible to do with a single tweak. I have been looking at the source code and nowhere I see an option of font color (see here for a list of all possible options). This could be easily added, and you can ask for this feature to the LightDM team joining the mailing list here. I strongly recommend that, as it would also help other users in the future.
Now, here are three possible solutions.
Use high-contrast. This might or might not affect your background image, depending on what it is. Assuming you have
sudo powers, go to
/etc/lightdm/ and open a file called
lightdm-gtk-greeter-ubuntu.conf or something related. Then add
high-contrast=true to the end of the file. Save and restart.
Change the theme of LightDM. This is also on the same file, under
theme-name=.... If you happen to know available theme names, you can manually replace it there with an alternative one. Yet, it is easier to use a GUI-based manager. For example, try this one:
sudo apt-get install lightdm-gtk-greeter-settings
Then, go to settings, open the LightDM GTK+ Greeter app, and select your preferred theme. There are also plenty of themes online.
sudo apt-get install lightdm-webkit-greeter
To use (according to this web) "copy the files located in
/usr/share/lightdm-webkit/themes/webkit, and create a new folder there (such as
/usr/share/lightdm-webkit/themes/mytheme". Place your created/downloaded theme there.
I hope this helps.