It sounds like you want Zoho CRM. There’s a leads page that everybody can access (although you can also limit who can view what, such as if you had multiple sales teams and had to divide leads among them)
There’s also many options for security management (https://www.zoho.com/crm/help/security/), including control over what users can view and edit. Exporting data from your system is an administrator tool, so it won’t be available to anyone who’s not an administrator.
Hope that helps!