Have you looked at this Perl script? I haven't used it - just did a quick search for mysql to sqlite migration and it popped right up.
Edit (after you replied to my comment):
The reverse direction is dealt with here.
If you are going to do it repeatedly and if data structure changes are to happen, maybe you would be better off using something like Django (albeit in a very hackish way). With it I would:
# This three lines are done once
django-admin.py startproject mymigrationproject
cd mymigrationproject
./manage.py startapp migration
# The following lines you repeat each time you want to migrate the data
edit settings.py and make the changes to connect to MySQL
./manage.py inspectdb > ./migration/models.py
edit ./migration/models.py to reorder tables (tables in which other tables depend on top)
mkdir fixtures
./manage.py dumpdata migration > ./fixtures/data.json
edit settings.py and make the changes to connect to SQLite
./manage.py syncdb
./manage.py loaddata ./fixtures.data.json