Bowl a rectangular quine
Python 3, 89 bytes

a='a=%r;b=%r;p=\\';b='print;p(a%(a,b));';p=\
print;p(a%(a,b));c='c=%r;p(b+c%%c)';p(b+c%c)

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The Levenshtein distance is 38, which is 86.36% of 44.
Explanation:
This is similar to the standard quine s='s=%r;print s%%s';print s%s. I had to try a lot of combinations and modifications in order to find my program. Creating the function p was used to make the second line shorter. The \ on the end of the first line is a line-continuation character.
a
a='a=%r;b=%r;p=\\'

A string template that results in the first line

b
b='print;p(a%(a,b));'


String that represents the first part of the 2nd line

p
p=\
print


Shorten stuff, change lengths

line 1
p(a%(a,b))


Print the first line

c
c='c=%r;p(b+c%%c)'


String representing itself plus the part after that prints b

line 2
p(b+c%c)


Outputs the second line