I'm not aware of Zabbix being used anywhere with customers, but I'm sure someone will let you know if it is. That aside, the use of Event Manager in Service Desk is purely driven by the capability of the monitoring tool to be able to call a web service or run a local exe file with some passed parameters. If Zabbix is capable of either of those then you should be ok.
I have used Landesk's LPM to do all kinds of cool stuff, it should be able to work with just about anything. It has Web Service, e-mail, and database listeners with all kinds of automation and process. Never heard of Zabbix but I would find it hard to believe LPM could not get data from it.
We also have SolarWinds and have recently procured Zabbix tool just curious if you got this off the ground for LDSD EM.
Just to add to Andy Parkers comments you will also need to check you are correctly licensed for Event Manager in order for it to create new lifecycles. To check, just open Event Manager in the Console and confirm you can see the "Add Network Source" action in the middle-top action panel.
If you can't you'll need to check with your Ivanti Account Manager or licensing team to see if you are entitled to it. You should have it with a TUM or Enterprise license or maybe because you purchased the module separately as an add-on.
All installations include Event Manager but with different levels of support for the "sources".