If you are looking for a free CRM with lead management, Bitrix24 is exactly what you need. The definition of lead management process is simple - a series of steps that help you convert a potential client into a paying customer.
What lead management tools are available in our CRM? First, lead capture. Yes, you've got to got leads somehow inside your CRM, and hopefully the entire process will be automatic (web to lead, email to deal, call to lead, social to lead, etc - they are all supported). Then comes lead enrichment, gathering as much data about your potential customer as possible.
Then you have to distribute leads between your sales agents. Then you have to qualify or score leads, identifying prospects who are most likely to buy. You'll probably want to run automated marketing campaigns on your leads at this point as well. It could be a series of emails or Facebook/Adwords campaigns targeting specific leads at specific stage in their lifecycle.
Then you'll need sales tools for your leads, such as quotes, invoices or product catalog. Finally, it all ends with lead analytics - trying to identify most profitable lead sources, analyzing bottle necks in your sales funnel and understanding your sales pipeline.
Yes, Bitrix24 has all those features, and most of them are absolutely free in cloud. It's not CRM vs Lead Management, and CRM with Lead Management. Because Bitrix24 is fully customizable and has on premise software editions with open source code assess, any custom CRM lead management process can be implemented and most common lead management automation scenarios are already implemented.
Bitrix24 CRM manual is available here.
If you are interested in buying self hosted editions of Bitrix24, which come with API, CMS and source code, and can be easily customized
and integrated with other tools, please download trial version here.