You can try temporary setting the lansweeper server in debug mode:
1. Stop the Lansweeper Server service on your Lansweeper server.
2. Open the following file on the server with Notepad or another text editor and replace this with this: Program Files (x86)\Lansweeper\Service\Lansweeperservice.exe.config
<appSettings>
<add key="debug" value="0"/>
</appSettings>
<appSettings>
<add key="debug" value="1"/>
<add key="LogHelpDeskConnection" value="7"/>
</appSettings>
3. Restart the Lansweeper service.
4. Send new emails.
Then have a look at Program Files (x86)\Lansweeper\Service\EmailLog.txt, as present on your Lansweeper server.
I hope this could help.