Ginga Eiyuu Densetsu, Magic Knight Rayearth II Recommendations
The atmosphere I find quite similar, darker with lots of drama and spacecraft battles and epic instrumental music. Thematically they're bit different (not as much as you'd think though), but MKR II also has depth despite being shoujo. Watching it requires watching the first season though, which is rather generic shoujo/magic adventure and can be repelling to some.
Both deal with the problems of Autocracy. MKRII takes focus on the personal relationship difficulties of an autocrat, while LoGH downplays this and focuses on national-level politics. The MKRII approach is better in my opinion, as you get to actually feel the difficulty.
This series reminded me more of LoGH more than almost any other series, despite it's appearance. Politics between various factions set in space. The atmosphere is very similar, I guess it makes some sense as both series share an episode director. A panning shot of a space-faring craft, discussion on the current situation among various characters, combat in space where the fight has some kind of consequence on the political situation. You see things through the perspectives of characters in both sides of a fight. The first season of MKR isn't much like it at all but on the other hand is a great adventure