Итак, методом научного тыка, а проще говоря перебором всех длл-ок начиная с версии 3.3.7, установил, что LIKE сломали при переходе с версии 3.3.17 на версию 3.4.0
Версия 3.3.17 без проблем работает с поиском LIKE по части слова на кириллице.
Вот описание изменений:
2007-06-18 (3.4.0)
Fix a bug that can lead to database corruption if an SQLITE_BUSY error occurs in the middle of an explicit transaction and that transaction is later committed. Ticket #2409. See the CorruptionFollowingBusyError wiki page for details.
Fix a bug that can lead to database corruption if autovacuum mode is on and a malloc() failure follows a CREATE TABLE or CREATE INDEX statement which itself follows a cache overflow inside a transaction. See ticket #2418.
Added explicit upper bounds on the sizes and quantities of things SQLite can process. This change might cause compatibility problems for applications that use SQLite in the extreme, which is why the current release is 3.4.0 instead of 3.3.18.
Added support for Incremental BLOB I/O.
Added the sqlite3_bind_zeroblob() API and the zeroblob() SQL function.
Added support for Incremental Vacuum.
Added the SQLITE_MIXED_ENDIAN_64BIT_FLOAT compile-time option to support ARM7 processors with goofy endianness.
Removed all instances of sprintf() and strcpy() from the core library.
Added support for International Components for Unicode (ICU) to the full-text search extensions.
In the Windows OS driver, reacquire a SHARED lock if an attempt to acquire an EXCLUSIVE lock fails. Ticket #2354
Fix the REPLACE() function so that it returns NULL if the second argument is an empty string. Ticket #2324.
Document the hazards of type conversions in sqlite3_column_blob() and related APIs. Fix unnecessary type conversions. Ticket #2321.
Internationalization of the TRIM() function. Ticket #2323
Use memmove() instead of memcpy() when moving between memory regions that might overlap. Ticket #2334
Fix an optimizer bug involving subqueries in a compound SELECT that has both an ORDER BY and a LIMIT clause. Ticket #2339.
Make sure the sqlite3_snprintf() interface does not zero-terminate the buffer if the buffer size is less than 1. Ticket #2341
Fix the built-in printf logic so that it prints "NaN" not "Inf" for floating-point NaNs. Ticket #2345
When converting BLOB to TEXT, use the text encoding of the main database. Ticket #2349
Keep the full precision of integers (if possible) when casting to NUMERIC. Ticket #2364
Fix a bug in the handling of UTF16 codepoint 0xE000
Consider explicit collate clauses when matching WHERE constraints to indices in the query optimizer. Ticket #2391
Fix the query optimizer to correctly handle constant expressions in the ON clause of a LEFT JOIN. Ticket #2403
Fix the query optimizer to handle rowid comparisons to NULL correctly. Ticket #2404
Fix many potential segfaults that could be caused by malicious SQL statements.
2007-04-25 (3.3.17)
When the "write_version" value of the database header is larger than what the library understands, make the database read-only instead of unreadable.
Other minor bug fixes

Из него конечно мне мало что понятно, но все же. Возможно возвернуть взад поддержку поиска в крайней версии?