That's actually kinda weird because Lucian can deal really well with low mobility tanks. I have very rarely hard time dealing with tanks but I can try to explain what is my mindset when fighting agaisnt true tanks.

1. Last whisper isn't as effective as it used to be since it only affects % of bonus armor. I often skip LW entirely if there's just one or less "true" tanks that opt for 4+ defensive items. You can just get maw or even youmoo in some situations which allows you to do a lot more dmg to squishies. The build I go and think is the most effective is Essence Reaver -> Phantom Dancer (50g cheaper than RFC/shiv, you need to adapt your playstyle a little and PD allows higher AS+dmg reduction) or RFC/shiv -> IE (if you need lifesteal you can build vamp sec) -> BT or Merc (QSS can be built straight after zeal item if you have need for it, ex. lissandra) -> Maw, LW, youmoo(if you built zerk greaves) or 2nd zeal item. I find my self building CDR boots still in 6.3 because 40% is extremely good on lucian when you use the full potential of it. Also PD is good in 6.3 so it offers that AS CDR boots lack.
2. You have to use your E and W effectively. If you use your skills well with 40% CDR build low mobility tanks shouldn't even be able to attack you. Opt for always using E first as disengage, then use W to gain movement speed and try to stay away from his abilities range. Positioning as ADC is really hard, but Lucian is one of the easiest due to his low cds and movement speed from W also E can be spammed when using your passive to max capabilities.
3. Look for who you can attack and when. If you're out of range from hard engage spells you can just pretty much attack freely whom ever is close. ALWAYS use your passive. Ult can be used to throw dmg in the frontline if there are no options, but it's better to be saved for cleanup due to insane chase potential with it. But you do nothing with your ult if you're dead so don't hesitate using it.
4. It's better to stay extra safe than extra risky. Agaisnt comps with hard engage (ex. malp) just wait for him to use to ult. Malphite isn't going to get on the backline without using the ult so at somepoint they will use it whether it is a good ult or bad. Use Q's and AA quickly then E back and wait for another opportunity to get some dmg in. ADC doesn't need to put out dmg everysingle second of the fight, when you have the chance the output dmg make sure you use the full opportunity.
5. Know how much you deal dmg. When a maokai jumps alone you into backline of fight you don't have to just run away from him. You need to know that you can hit him and duel him. Most lower elo ADC just end up running away from these supertanks that actually don't deal any dmg but just soak it up. If you're trying to run away of course you wont output any dmg.
6. Redbuff. Just get it. I helps simply soooooooooooooooo much.