The latest DeaDBeef 0.5.5 doesn't seem to have this problem - the empty space disappears and the player looks fine with lyrics: but only as long as the File Browser plugin (or maybe some other plugin) is not used. Similar problems with other plugins are very possible.
The cause of this is explained by the author of infobar (here) as follows:
"Unfortunatelly, deadbeef doesn't provide API which allows to integrate third-party UI plugins into its interface (situation gonna be changed with release of version 0.6.0). In this situation infobar and filebrowser plugins use hacks to integrate themselves into deadbeef's interface and can't work together."
In v. 0.5.6 the Filebrowser and the gtk2 version of Infobar have the same incompatibility. But there is a gtk3 version of Infobar, and Deadbeef v. 0.5.6 has a gtk2-gtk3 GUI switch.
Installing Infobar gtk3 and the File-browser, which is gtk 2, will result in using the two plugins alternatively: in the gtk2 GUI of Deadbeef only the file-browser will be visible, in the gtk3 GUI, only the Infobar. Switching between GUIs will switch between plugins too.
When lyrics are not found by Deadbeef/Infobar, use Foobar in wine and install the lyrics grabber addon.
But usually would not need that (the difference with Foobar is that it embeds the lyrics into the file: Deadbeef displays them from internet)