If you want to handle the output format explicitly via strftime, there are some things to keep in mind:
Instead of hard-coding 999, you should use %L to get the actual milliseconds:
time = Time.parse('2020-07-02 03:59:59.999 UTC')
#=> 2020-07-02 03:59:59 UTC
time.strftime('%Y-%m-%dT%H:%M:%S.%LZ')
#=> "2020-07-02T03:59:59.999Z"
Use combinations for common formats, e.g. %F for %Y-%m-%d and %T for %H:%M:%S:
time.strftime('%FT%T.%LZ')
#=> "2020-07-02T03:59:59.999Z"
If you are dealing with time zones other than UTC (maybe your machine's local time zone), make sure to convert your time instance to utc first:
time = Time.parse('2020-07-02 05:59:59.999+02:00')
#=> 2020-07-02 05:59:59 +0200
time.utc
#=> 2020-07-02 03:59:59 UTC
time.strftime('%FT%T.%LZ')
#=> "2020-07-02T03:59:59.999Z"
or to use %z / %:z to append the actual time zone offset:
time = Time.parse('2020-07-02 05:59:59.999+02:00')
time.strftime('%FT%T.%L%:z')
#=> "2020-07-02T05:59:59.999+02:00"