Terraria – How to move water/lava in Terraria

There's rocket boots you can get for going up faster.

Each Anklet of the Wind you equip adds 10% to movement speed. (But as of 1.06, they no longer stack, though you should be able to have one Anklet and one Aglet)

Hermes Boots increase movement speed by 100%, but take a while to accelerate.

With 1.1 the previous answers are no longer correct. Since you are digging down through the lava, redirect some water into your mineshaft. As you dig into the lava, the water will hit it and form obsidian walls to hold the lava back. You will need a nightmare pickaxe or better to dig out the obsidian that's in your way.

Another alternative is to use an obsidian skin potion (and maybe a gills potion) to safely swim to the bottom of the lava and dig a drain for it.