What transport protocol are you using?
If JMS, couldn't response 1 of 2 go on the wire immediately, and response 2 of 2 delay with a Think Time of 10 seconds. The Think Times control the timing and DevTest controls everything else OOTB.
If using HTTP protocol, I don't know how you are sending two responses since the protocol standard is to close the socket after a single request / response pairing.
However, if your second response is actually a 'callback' in the form of a request, you could add steps to the model that retrieve the second response (i.e., lisa_vse_response.get(1).getBodyAsString() ), send the first response, thread sleep for 10 seconds, send the response as a Webservice / REST request step, then loop to LISTEN.
For your date/time issue, are you saying that {{=doDateDeltaFromCurrent("yyyy-MM-dd 'T' HH:mm:ss.SSS", "0D");/*2016-07-06 T 04:15:52.063*/}} is not working for you? I could see a potential issue using: {{=doDateDeltaFromCurrent("yyyy-MM-dd 'T' HH:mm:ss.SSS", "10S");/*2016-07-06 T 04:16:02.063*/}}
You might add a date/time filter in the VS Image Response Selection Step to create a property representing the current date/time and another filter representing the current date/time + 10 seconds using your simple date format? Then in your VSI, replace the date/time stamp with the appropriate {{currentTime}} and {{currentTimePlus10}} property, respectively. This may not be a 100% accurate way to correct the date/time issue, but it could be reasonably painless to try.
Lastly, for HTTP, I have delegated the second "response" off to another VS via the Shared or Persistent Model Map. This 'worker' VSE does not have a LISTEN step, rather it wakes up, iterates the Model Map, sends what it needs to, goes to sleep and wakes up again after 'n' amount of time. This is a technically complex approach because your services have to manage the information going onto / off of the Map. And, testing/debugging is a bit more difficult. But, there are times and reasons why a functional VSM may not be able to thread sleep for 10 seconds in order to get the 2nd HTTP "response" on the wire.