How did the south's fortunes change after Lee took command of the Northern?

Rapidly for the better.

In the Summer of 1862, Lee took the Confederacy to its 'high watermark' with a string of victories, ending with Second Bull Run.

This encouraged him to try to invade Pennsylvania, but a chance accident cost him the next battle - Antietam, costly in casualties and in credibility for Lee. For the British were judging the whole viability of the Confederate rebellion by the success or failure of this campaign.

When they got the news of Lee's defeat, the chance of British intervention was missed.