I dare say that powershell might be a better way to find this than LEM, for a few reasons I will get into later but to the immediate question:
Windows service starts are associated with eventid 7035, so if you filter against SID *7035* that should get you all the service start events that you are recording. Probably filter it down further with the source account.
The tricky part now being, is auditing turned on for 7035 in your environment? If it wasn't already on then you won't have any events to check until the next time the server reboots, which could be a real pain. In theory this should show you all the start events you have that ran under the admin account:
In practice I don't think most people have taken the extra step to tell windows to audit service starts so you will find that this info is not in the logs. As a general rule if you can't find something in LEM you should double that this info exists in the original log source because I cannot tell you how many times people asked me to spin up rules for them to identify some event, then got irritated that they couldn't find it in LEM, and then I pull up the source data and prove that they don't log that event in the first place. LEM is essentially just a fancy log aggregator so if you don't have a piece of data without LEM then it still won't be there after you set up the appliance.
If it were me i'd probably build a list of computers and run a powershell script like discussed here
PowerShell: How to get logon account of services on remote computer