In episode 6 of The Irresponsible Galaxy Tylor, a narrator tells the story of Justy Ueki Tylor. He begins by describing the events of The Irresponsible Captain Tylor, before stating:
[…] He returned Goza XV to Raalgon, and brough about a temporary peace.
However … Ceasefires are easily broken. Tylor and Ru Baraba Dom had a battle for control of the galaxy. Tylor won the battle completely, but the Grand Duchy of Ashuran conquered the galaxy. Raalgon and the United Planets put together a joint front, and in the final battle with Ashura, used their ultimate weapon, Suou to win, and bring about eternal piece. Tyler [sic] became president of the Raalgon Republic!
Tylor declared war on the United Planets, and had a final battle with Makoto Yamamoto. Tylor won, uniting the galaxy, and became the pan-galactic emperor! Ensured by Tylor's success, the Pan-Galactic Empire flourished. But now, humanity is in its twilight on the sidereal mega-structure.
[Text taken from the current version of the Crunchyroll subtitles. There may be mistakes: I hear what appears to be ゴザ十六世 in the audio, rather than ゴザ十五世. The narrator is also clearly referring to Azalyn, who is Goza XVI. Paragraph breaks are my own.]
Did the events described here actually happen in the Irresponsible Captain Tylor franchise, or was this all something that the narrator made up (or alternatively, something that was made-up for this spin-off)? Such events do not seem to happen in the OVA, and I also cannot find any reference to a confrontation with Ru Baraba Dom on his wiki page. But it seems possible that there may be light novel content that non-Japanese fans may be unaware of.