It looks like that's the downfall of clinching too quickly. In 1985, the LCS was extended to seven games, and there were only six instances of LCS sweeps:

1988 Oakland over Boston
1990 Oakland over Boston
1995 Atlanta over Cincinnati
2006 Detroit over Oakland
2007 Colorado over Arizona
2012 Detroit over New York

Out of the six teams that swept the LCS, only one won the World Series.

In 1988, Oakland clinched on a Sunday, and the World Series started the following Saturday. Oakland lost the World Series 4-1.

In 1990, Oakland clinched on a Wednesday, and the World Series started the following Tuesday. Oakland was swept.

In 1995, Atlanta clinched on a Saturday, and the World Series started the following Saturday. Atlanta won the World Series in six games.

In 2006, Detroit clinched on a Saturday, and the World Series started the following Saturday. Detroit lost the World Series 4-1.

In 2007, Colorado clinched on a Monday, and the World Series started the following Wednesday. Colorado was swept.

In 2012, Detroit clinched on a Thursday, and the World Series started the following Wednesday. Detroit was swept.