If a lead becomes inactive and no longer needs your attention, you can clear it from your Active Leads Queue by archiving it. The lead will still be in the system, but it will remain hidden until such time as they send another message.
To archive a lead, click the "More Actions" icon in the Lead Profile, and choose "Archive" from the dropdown. A popup will appear in which you must specify your reason for archiving.
If you need to find a lead after you've archived it, you can either use the search feature, or look for it in the Archived Leads Queue in your Lead Feed. To reactivate the lead and return it to your Active Leads Queue, simply choose "Unarchive" from the same dropdown.