Lava Boat 1.14.4

You could make the mob turn lava into a solid block for some seconds (kinda like frost walker)? But it would feel a bit weird, I don't think you can properly recreate the Strider from 1.16

Fire resistance maybe?

I would look at the vanilla boat code. I haven't seen it, but recreate the boat. And I believe you might get a "bug" where the player is set on fire (do to the lava), so I would put a bit of code that checks for that in my event handler and cancels fire tick event. But theoretically, if your entity works and is like a boat what you want, this code block is not really necessary, just kinda another check. 

Probably something like this (THIS MAY NOT WORK SO TEST FOR YOURSELF, I CAME UP WITH THIS IN MY HEAD)

    public void onPlayerTickEvent(TickEvent.PlayerTickEvent event)
    {
        PlayerEntity player = event.player;
        if (player.isBurning() && player.getRidingEntity() instanceof YourCustomEntity)
        {
            player.extinguish();
        }
    }

Good Luck!

Or you could edit the entity's mounted entity Y offset to the point that the player wouldn't be touching the lava while riding it.