Does anyone know how to find the lava suit thingy?

The only suit in the game that lets you through lava without damage is the Gravity Suit, which you recieve after passing the test in Chozodia. The test is where you have to shoot a glowing emblem within a mirror platelet that a Chozo Statue carries. It's rather easy if you ask me.

The "run fast thingy" is the Speed Booster. You recieve it after defeating Kraid.

To get the speed booster you need to beat the dragon
( His name is kraid)and you might want to add where you are. And there are two suits in the game the varia suit and the gravity suit. The varia suit halfs damage and lets you walk in hot rooms and lets you move in acid to get it you have to beat kraid go to norfair speed boost to the right as far as you can go to drop down to get the High jump boots and you go to the chozo statue below and then follow the signal to brinstar and when you hit a room with one enemy in front of you and a bunch blocked from you above you. go up by destroying the blocks kill the enemies and watch out don't go to far to the left or you will fall back down. Then once you have reached the top you can go left and then you let the little bugs kill the sacs and go to the far left to get the varia suit. To get the gravity suit you kinda get in in kraid I thing but to activate it you have to beat the second to last boss. It stops lava damage and lets you move better in water lava and acid.