The ArcGIS License Manager can function on the same system as other vendor's license managers and vice versa, although it is not recommended as a general practice by Esri. In the majority of deployments, this 'just works'.
When it doesn't work, the reason is usually one of a few issues:
• Port Conflict (netstat -an to see open ports). See this link to solve this issue: Microsoft TechNet - Netstat
• Lmgrd daemons referencing newer vendor daemons (such as ArcGIS.exe). Replace all instances of 'lmgrd' within each vendor's installation directory (i.e., replace C:\Program Files\ArcGIS\License10.0\bin\lmgrd.exe) with the latest release of lmgrd available here: Download page for FlexNet license server managers
The ArcGIS License Manager utilizes the 32-bit lmgrd daemon. Be sure to download this version of the lmgrd daemon.
Be sure that each vendor's license manager software is referencing the appropriate lmgrd process. For example, in Windows, the ArcGIS License Manager Service should reference:
License Manager Guide
Other vendor's license manager software should reference the lmgrd.exe process in their vendor home directories. This issue commonly manifests itself when these values are not configured properly.
** ADDITIONAL INFO **
There are multiple ways to configure FLEXnet licensing servers to function concurrently on the same system. The above information is one of many possible methods to accomplish this task. See the following documentation for more details: License Administrator Guide
It is highly recommended that anyone who manages multiple license managers take a look at the above guide paying particular attention to Chapter 17 - Managing Licenses from Multiple Software Publishers.
Also, the ArcGIS License Manager 10 Reference Guide is always an excellent source of information. Many of the answers to the most common setup and operation questions can be found at this site:License Manager Guide
If the License Manager is already installed, the reference guide may be accessed locally or you may access the most up-to-date information on the License Manager via the ArcGIS Resource Center (see Related Information below).
Example: Start > All Programs > ArcGIS > License Manager > License Manager Reference Guide