There is a field on the Lead object called "Last Activity". This might be what you are looking for and it can be used in a Report. You can set a filter on the report where Last Activity = Last Week. For a more complex solution you would need to use some sort of rollup tool to scan through the Activity history and calculate the exact logic of the way you want to track your type of activity.
"Last Activity shows when someone in your Organization last did something related to the record. It represents one of the following:
The latest Due Date of the closed tasks on a record.
The latest Date of events on a record.For example: If you have multiple Activities on a record, the Last Activity would show the Due Date which is farthest of all. So, if the Due Date on all Activities are 1/01/2015, 2/01/2015, 3/01/2015, the Last Activity would show 3/01/2015" on the report and would take this date into consideration when filtering the List Views. In List Views and "Reports, the Last Activity is labeled "Last Activity." Last Activity is not available to add to the Page Layout."
https://success.salesforce.com/ideaView?id=08730000000jjoFAAQ
