The Lead Test →
How good do I need to be to lead climb?
Most gyms have a policy of requiring lead climbers to be very comfortable on 5.9 routes before they take a lead test. This isn't a hard and fast rule -- of course it's difficult for anyone but you to say what you're comfortable on anyway -- but the requirement does serve as a good barometer for your readiness to get on the sharp end of the rope.
The 5.9 requirement basically exists to make sure you have the fundamental knowledge and confidence that comes with the basic movements of climbing. It's not fun, nor is it safe, for beginner climbers to attempt lead climbing without the endurance and strength that comes with adequate practice. For this reason, some gyms will also impose a six month rule on new climbers: If you haven't been climbing consistently for six months, the gym may want you to take a lead class or wait until you've gathered more experience.
Another reason the 5.9 grade is the common threshold for lead climbing is because routes suitable for safe leading are going to be somewhat overhanging, and it's not easy to contrive <= 5.8 routes that meet this criteria.