When I assign the lead to someone it disappears from my leads. How could I send lead to person in system and leave it in my list (to view)
This can be managed using Roles
Create a role = “Manager”
Here in the rules Lead - Edit, Delete, View and List are set to all
Create a role = “Basic User”
In these rules for Lead - Edit,Delete,View and list are set to Owner
Any user in manager will see “all” leads
Any users in Basic user will see their Own leads
If you are an admin user you are above Role management and see/edit everything
Thanks 
Another reason for this is you may have a default filter on your Leads to only view “my items”