How would I replace multiple letters in a string with different letters?

Last post, I figured out how I could replace a letter with another letter using gsub. Try running this in the command bar:

local str = "Hello there! How are you doing? I'm feeling great today!" 
local changedString = str:gsub("a", "z") 
print(changedString)

Now it would print that string, but all the A's get replaced by Z. I do know how to do that, but how would I replace multiple letters? For example, I turn the A's to a Z, the B's to a Y, and the E's to an X.

Here are 2 things I have tried:

local str = "Hello there! How are you doing? I'm feeling great today!" 
local changedString = str:gsub("a", "z") 
changedString = str:gsub("b", "y") 
changedString = str:gsub("e", "x") 
print(changedString)

Now this wouldn't work because every time it would change the changeString thing, it would overwrite it with the normal string, but a letter replaced by another. And only 1 letter replaced. Other thing I tried:

local str = "Hello there! How are you doing? I'm feeling great today!" 
local changedString = str:gsub("a", "z") 
changedString = changedString:gsub("b", "y") 
changedString = changedString:gsub("e", "x") 
print(changedString)

Now this would replace multiple letters, yes. But say like in a line, the script would replace all the E's with a Y, then in the next line, it would replace all Y's with an O, and I want the changed letters not to change again. Thanks!