The reason for using avgas has nothing to do with lead content or high octane. Modern small engines need neither. The main advantage of avgas is its long-term stability. Avgas has a maximum Reid Vapor Pressure of 7 psi, primarily to prevent vapor lock. Historically, mogas had a much higher vapor pressure, but typical summer grade gasoline sold today has a relatively low RVP. In some areas, summer grade gas is limited to 7 psi RVP, same as avgas. In California, RVP is limited to 7 psi year-round.
A lot of companies are working on replacements for Avgas, but the real problem isn't replacing the lead so much as is the small market for aviation gasoline. There's not a big incentive for companies to come up with a replacement for a product that's not a major part of their bottom lines.