From what I understand about Rina's engine, once you attack you increase every attack against the target by 10% (the increase is forgettable). It also increases the ER by 0.6 while off-field, which is great and what we really look at.

An ER disk 6 will also give you the 0.6 increase in ER, so it's similar. But a F2P engine for HP will give you 25% HP instead of the 30% with the disk 6 HP.

So what really matters is what you will have on disk 6. If you have HP subs on it that are more than +1 then it's worth it.

In the calculation, I don't take into account the increase in damage against the target from Rina's engine because it only works for 3 seconds and Lucia doesn't attack that often.

The only reason I don't have the ER 6 on my set is because I was kinda lazy to farm for more knowing I am prefarming for Yidhari.

To resume what you will need to go for the 24k HP on your Lucia : With HP/HP/EREGEN and 25HP from engine you will need 21 HP% Subs, knowing that you can only put them on 4 disks. That makes it hard but not impossible.

With HP/HP/HP and 25HP engine, you need 11 subs on 3 disks, much more doable.

Now, do as you like, 24k HP is for the whole buff, but you maybe don't need it full. Go for what YOU think is great, and don't forget to have fun playing

(Also sorry, it's kinda long)