I've been on Levaquin several times, twice for five days and once for ten days.
Tendon rupture occurs very infrequently, in only 0.1% to 1% of clinical trials:
http://www.levaquin.com/sites/default/files/pdf/levaquin.pdf#zoom=100
I did easy training sessions of 30 to 60 minutes while on Levaquin and never had a problem with tendon rupture. Then again, nine-minute miles aren't likely to cause ruptures! It is not as if Levaquin dissolves tendons.
The greater concern is that if you're on an antibiotic as strong as Levaquin, you must have a fairly serious or resistant infection, which will itself challenge your immune system and make you much more tired. The more common side effects of Levaquin -- headache, insomnia, and digestive distress -- also make it harder to do workouts and recover from them.
Once the infection is mostly gone and the desire to run returns, easy running appears to be a fairly safe activity. Just don't let it exhaust you to the point that your immune system is compromised.