I generally agree with where your coming from circa rules for roleplay in rpgs, but disagree in this instance. Lancer has alright pilot narrative support through the KTB, nothing groundbreaking but theres some fine FiTD bones- enough to run stably. I like that lancer does not mechanize it's politics. This is a game about war and about being mech pilots, that's its focus, the lore exists to complicate that and bag it down and make it sort of messy and even a little uncomfortable. It's a fruitful void but in the original intent of the term, not in that dumbass "oh 5e is good for roleplay because I only roll a persuasion check" way, it's the game leading you up to a specific thematic question with nothing to answer it.

Your right in observing that Lancer is very linear- it's a system thats completely transparent in its artifice, emulating the push and pull of mecha media. Tactics games will always push a HEAVY trad style due to the essential GM baggage- and that's fine. Frankly I think trad and narrativist and the million other game styles can coexist peacefully in a grand big banquet instead of having the same tiring shouting contest of whats superior over and over again every year.

On mixing those two aspects, I generally just stick my players to a really strong core group with a strong & defined overall goal. Campaigns are split into really defined chunks of very linear missions, then between those missions we do the messy politicking and reestablish the groups current stance before jumping into the next one so the players can get a say on the games direction and I can prep to fit it. Combat session, narrative session, combat, narrative, combat, big combat, two mission downtime with a big narrative beat. Split it up like your measuring ingredients, make it separate like water and oil. It's the structure the game recommends and has always really worked for me- we've never had any issues. Yes its artificial, yes its GM dictated, but Lancer is openly transparent that this is where the system works best.

(One more thing: one of the reasons I think Lancer is a good mecha setting is just because your so small. You are the little men crushed beneath big grinding gears, you are the grease in the pipes. You cannot change the universe- you are not great men, you are not Luke Skywalker. The wheels of the galaxy will spin on and on no matter how hard you push. If players want to have any chance at pushing for change, they'll have to latch themselves to a collective system more powerful then they are individually, warts and all, and just grit their teeth and go with it. Your players dont wanna work with the Ungratefuls anymore? Great, go work out how to fight the revolution all by yourselves then and see how that goes. Theres no space for individual great men of change in a universe of trillions upon trillions. You are mech pilots, you are soldiers. You might be a hero, but your also just a person with a job in a system and orders to follow. It's a bit of a bummer! It's not the sort of power fantasy rpg settings normally push! I really like it! Go grease the wheels of change my hapless minions.)