As reported on the Spigot resource discussion thread, and confirmed by me, players take damage after riding down elevator. This occurs regardless of speed.
Spigot 1.12.2

Confirming that it occurs with two passengers. Though, I am unable to accurately predict who will take damage. Sometimes one player will survive, sometimes both players take damage.

This is solo. I have not yet tested with multiple passengers.
Thank you.

I still can't duplicate it, can you send me a list of plugins?

OK, looking at my plugin list again, and thinking about how the fall damage seemed oddly delayed, made me realize the issue. This is a conflict with NoCheatPlus.

If you see here, NCP is trying to enforce fall damage in survival.

I have confirmed that disabling this check resolves the Lift issue.

Would there be a way of making the two play nicely, without having to turn off this protection?

I realized that I am using one of the popular newer configs, this one.
Unsure if that is making any difference.

Edit:
NoCheatPlus | 3.16.1-SNAPSHOT-sMD5NET-b1143
CompatNoCheatPlus | 6.6.5-RC-sMD5NET-b90

I tried the above version of NoCheatPlus with it's default config, and couldn't even ride the elevator.

18-04-10 09:03:24 [INFO] username failed SurvivalFly: tried to move: -233.97, 90.06, 152.95 -> -233.97, 89.56, 152.95, d=0.50 (data_reset+vdistrel). VL 105.
18-04-10 09:03:24 [INFO] username failed SurvivalFly: tried to move: -233.97, 90.06, 152.95 -> -233.97, 88.99, 152.95, d=1.07 (data_reset+vdistrel). VL 462.
18-04-10 09:03:27 [INFO] username failed SurvivalFly: tried to move: -233.97, 90.06, 152.95 -> -233.97, 89.56, 152.95, d=0.50 (data_reset+vdistrel). VL 1519.
18-04-10 09:03:27 [INFO] (CONSOLE) Kicked username: Kicked for flying (or related)

Edit: This was already reported in #148

Should be fixed