For all their complaints about not getting a chance to "punish" the Draconis Combine, the Lyran Commonwealth very much did just that during the Fourth Succession War- at the same time as Hanse was ravaging the Capellan Confederation, the Lyrans were belting the hell out of the Combine.
Hanse had Justin and Alex. Katrina had Takashi Kurita. Due to his focus on the Wolf Dragoons and Theodore's marginalisation in the DCMS, the Lyrans were able to capture fifty worlds. That they were then forced to turn around and release most of those gains to the Free Rasalhague Republic is largely irrelevant.
They had another go at it in the War of 3039, but this time Takashi wasn't holding all the cards and the Lyrans were quite steadfast in their refusal to see reason and/or co-ordinate with the AFFS. Even so only minor changes would have seen a drastically different result- usesless as Nondi Steiner was, things were still bubbling along quite nicely for the Lyrans under her command. With even the slightest of differences, the War of 3039 would have been as devastating as the Fourth Succession War.
Unfortunately, where it all broke down was in Lyran resistance to the merger, be it military or otherwise. Katherine Steiner-Davion and her antics are probably the most visible example, but it was endemic.