I read that The Lucy Show was second in the Nielson Ratings in the 1967-1968 season. Why did they change it to Here's Lucy if it was doing so well?

There were a couple of reasons. Lucy felt that the series had basically run its course. The writers were running out of ideas, the show wasn't nearly as good quality wise, and she felt it was basically time after 6 years it was time to end the show. But the number one reason is she wanted to do a show with her reallife children playing her on screen children. She couldn't do that on "The Lucy Show" since she already had on screen children on "The Lucy Show" even though they were written out after season 3. So changing to a new show allowed her to create a new plot and new refreshing spin on "Lucy" with her children involved.

Also, she had sold Desilu that year. If she had continued with The Lucy Show she wouldn't have had as much creative control. So she switched production companies I believe.

Exactly! She sold Desilu to Paramount or Gulf and Western, and with the sale of the studio went the show, so she had to create a new format, hence Here's Lucy!