The number of zones in a reflow oven is only one of many aspects of the oven that will influence a successful lead-free process. The oven stability, zone separation capability, heat transfer rates and uniformity, max heater capability, and many other variables are also critical.
To generalize, additional zones, both heating and cooling, are very helpful when running lead free production, and they are required as you mention to increase throughput. I have seen companies run lead free production in a small 5 zone oven, but that is rare.
The goal with any thermal process is to create an in-spec profile at the required throughput. As you know, the lead-free process window is both much tighter than the eutectic process, and it requires higher temperatures. An oven with fewer zones may require you to really fine tune the oven recipe in order to produce the required profile, if the oven is capable of an in-spec profile at all.
There are profilers and process optimization software on the market that enable you to identify those hard to find suitable oven recipes in a few seconds. Our company KIC is one of the suppliers for such products.