Use the following:
| inputlookup yourlookup
| eval earliest=strptime(End_Date + " " + End_Time,"%Y-%m-%d %H:%M:%S"), latest=strptime(Start_Date + " " + Start_Time,"%Y-%m-%d %H:%M:%S")
| return earliest, latest
That will give you the earliest and latest fields, and so you can pass them to your main query, like this:
Main query example
index=_internal [
| inputlookup yourlookup
| eval earliest=strptime(End_Date + " " + End_Time,"%Y-%m-%d %H:%M:%S"), latest=strptime(Start_Date + " " + Start_Time,"%Y-%m-%d %H:%M:%S")
| return earliest, latest
]
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