Python regex positive lookahead cannot split correctly

I've text consisting of sections. In each section:

• The title is in uppercase and may span multiple lines
• The body may have acronyms, so we cannot assume that uppercase words mark the start of each section

There may be zero or multiple line breaks between sections.

Example

import re

text = """
Lorem ipsum

THIS SECTION IS A SHORT STORY
1 Hello world
2 Bye bye
Side comment


NEXT SECTION SPANS 200
YEARS AND MANY COUNTRIES!

3 Joe Bloggs attended a NATO summit
4 John Doe heard...
THIS SECTION HAS NO
LINE BREAK / SPACE FROM
THE PREVIOUS ONE

5 Alice thought...
6 Bob visited...
""".strip()

re.split("\n(?=[^a-z]+\n+[a-z\d])", text)

I expected it to split the text by sections like this:

["Lorem ipsum\n",
 "THIS SECTION IS A SHORT STORY\n1 Hello world\n2 Bye bye\nSide comment\n\n",
 "NEXT SECTION SPANS 200\nYEARS AND MANY COUNTRIES!\n\n3 Joe Bloggs attended a NATO summit\n4 John Doe heard...",
 "THIS SECTION HAS NO\nLINE BREAK / SPACE FROM\nTHE PREVIOUS ONE\n\n5 Alice thought...\n6 Bob visited..."]

Instead, Python splits up each section as follows, which seems to contradict the lookahead assertion:

["Lorem ipsum",
 "",
 "THIS SECTION IS A SHORT STORY\n1 Hello world\n2 Bye bye\nSide comment",
 "",
 "",
 "NEXT SECTION SPANS 200",
 "YEARS AND MANY COUNTRIES!\n\n3 Joe Bloggs attended a NATO summit\n4 John Doe heard...",
 "THIS SECTION HAS NO",
 "LINE BREAK / SPACE FROM",
 "THE PREVIOUS ONE\n\n5 Alice thought...\n6 Bob visited..."]

Questions

Why does [^a-z]+ behave like a lazy match instead of greedy match?

What's the correct solution?

updated example

We can add a lookbehind to match a double \n (or split on \n\n if you don't need the trailing \n), and include digits in the set of characters.

re.split(r"(?<=\n)\n(?=[A-Z0-9 ]+\n)", text)

Or (?<=\n)\n(?= *[A-Z][A-Z0-9 ]*\n) to force at least one initial uppercase.

Output:

['Lorem ipsum\n',
 'THIS SECTION IS A SHORT STORY\n1 Hello world\n2 Bye bye\n',
 'THIS SECTION SPANS 200\nYEARS AND MANY COUNTRIES\n3 Joe Bloggs saw...\n4 John Doe heard...\n',
 'THIS SECTION IS ALSO A\nLONG STORY ABOUT EVERYTHING\nSINCE 1669\n\n5 Alice thought...\n6 Bob visited...']

regex demo

using a loop

import re

out = ['']
prev_header = True
for line in text.splitlines():
    if line:
        header = bool(re.fullmatch('[^a-z]+', line))
        if header and not prev_header:
            out.append(line+'\n')
        else:
            out[-1] += line+'\n'
        prev_header = header

Output:

['Lorem ipsum\n',
 'THIS SECTION IS A SHORT STORY\n1 Hello world\n2 Bye bye\nSide comment\n',
 'NEXT SECTION SPANS 200\nYEARS AND MANY COUNTRIES!\n3 Joe Bloggs attended a NATO summit\n4 John Doe heard...\n',
 'THIS SECTION HAS NO\nLINE BREAK / SPACE FROM\nTHE PREVIOUS ONE\n5 Alice thought...\n6 Bob visited...\n']