How to capture the last login date or last license acquired date for CLM?

The floatingLicenseLogFile.csv is generated in the server/logs directory.
The data is the form of :
     | license_server_url | ref_id | checkout_time | timeout_time |
license_type | user  | product_usage | acquisition_type |

From this csv, to know the last license usage from a user,  you could
a.  Sort the user data by name using the excel function and look at each user's last entry.
b.  Pivot the usage details and create a table as well.

Regarding the time mentioned in the additional comment for the question for modified:
It is the time elapsed in milliseconds since Jan 01st, 1970 or what is in
other words called as the epoch time.
You could use an epoch converter to know the time the value corresponds to. 
One such converter is here : http://www.epochconverter.com/

The time mentioned in the comment "1405377349240" translates to "GMT: Mon, 14 Jul 2014 22:35:49 GMT".

With the understanding that the time shown against MODIFIED field is referencing epoch time, you could convert the 120 days ago date to the epoch time and use it with a query on LICENSE_ASSIGNMENT table.

below is a sample query :
    select * from REPOSITORY.LICENSE_ASSIGNMENT L where L.MODIFIED >
'2015-06-30 20:01:24.706';
where MODIFIED is compared against the minimum date (120 days ago) that you wish to filter users on.
With the above query, you get a list of users who made use of a license in the last 120 days.

Now, with another query you could get a list of all users and work out the list of users whom you want to deny access.