No. You;ve switched the DB to simple recovery and back to full. Unless there has never ever, ever been a full backup taken (and if that were the case there couldn't have ever been any log backups running), all you need to do to restart the log chain is take a diff backup.

Sure, the diff's useless without the associated full, but databases that are important enough to get log backups get regularly scheduled full backups that are kept in safe places?