In your Console you have in your toolbox the option Alerting. Here are rules yuo can edit and deploy to managed devices which have realtime alerting and monitoring enabled in the agent. Look here http://community.landesk.com/support/docs/DOC-10653 for more general information on how to set up rules and mail alerts.
In the console, go to Configure - Inventory History and mark any inventory attribute that you want to monitor for changes, in this case you might want to do product name for Add/Remove programs. Set this for Alert and Inventory and you can set it to send an email and the histroy of that machine will show historical changes.
However, it will alert on all installs and uninstalls, not just those that were done by the user. There isn't a way to do this just for user software installations.
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Also, you can set up a rule in Alerting that will alert on Software Installations. If you edit for example the Default LDMS Ruleset, which is already send with agents by default, you can add an alert for Applications added or removed. This will be more real-time as it checks the client periodically, whereas the inventory history is depending on how often you run inventory scans.
As Mark says though, there is no way to distinguish between user and LANDesk software installations.