Black tea with lemon juice , is it good for health?

Yes, it is. Green tea would be even better.

A 2001 Boston University study has concluded that short and long-term black tea consumption reverses endothelial vasomotor dysfunction in patients with coronary artery disease. This finding may partly explain the association between tea intake and decreased cardiovascular disease events.

In 2006, a German study concluded that the addition of milk prevents vascular protective effects of tea.

Theaflavin-3-gallate, a theaflavin derivative found in black tea, could reduce the incorporation of cholesterol into mixed micelles.

Source (http://en.wikipedia.org/wiki/Black_tea)