I believe you're getting confused. There's no bit string reversal in DEFALTE, it just changes your shift slightly. Both MSB and LSB have their advantages and disadvantages.
I meant that with the bit ordering that DEFLATE has (the root in the LSB), you can't simply add/subtract 1 to each code to get to the next one, because the carry goes the wrong way.
With a normal (ascending) canonical code, e.g. "2 codes of length 3, 2 codes of length 4" becomes
000
001
0100
0101
when read into a register. With DEFLATE, the same codes would look like
000
100
0010
1010
so you need to pre-rotate the bits in your lookup table to match.
As always, ryg has great posts on this stuff: https://fgiesen.wordpress.com/2018/02/19/reading-bits-in-far...