The different editors handle this sort of thing differently. I suggest using CKeditor because it doesn't mess with the markup as much as TinyMCE.
Using CKeditor, click the "Source" button and paste your code, then immediately click the Save button. This will save your code without modifying it at all.
Alternatively, if this is something that you aren't going to be changing at all. Try this:
Create an HTML file with this code inside of it, nothing else, just the code for LiveZilla.
Save the HTML file to \data\sites\[site number]\htmlfragments.
Add an instance of the HTML Fragment Include feature to your page.
Click the Edit link for the HTML Fragment Include module and then select the HTML file you saved in step 2.