LS generally doesn't need a preservative, because of it's alkaline enviroment not being conducive to microbial growth. BUT if you still choose to use one, please make sure that it will actually work in an alkaline environment. Most preservatives that i find soapers use for LS are not effective in a pH over 9. The following is a link to a list of 27 different preservatives and there actual ph range of effectiveness.
http://makingskincare.com/preservatives/
And if your testing your pH and it falls below 9, something is off, especially if you're using strips. Soap is generally mid range alkaline, and is skin safe between 9 and 10. Below 9, and your soap will fall out of solution, ie, cloud and begin to break down/separate. Above 10, and it's not skin safe. Cellular breakdown can occur above 10, and you won't even notice it. I know of one person who gets her soap at 8.5 with no issues, and she uses a meter to test. So I can't question too much there. But she's the only one I know of in other groups I'm in. But ph testing accuracy is a whole nother ball park, and not what you're asking for.
Now as for the preservatives in that list, some touch on the edge of working in soap, pH wise. They can go up to 9. My thought is, though that being that close to soap's minimum pH range, it could be debatable that they'd be effective, if you were to get your soap at 9..or even a smidge below. Nothing says that effectiveness is equal across the board. A preservative with a range of 5-9 might be less effective at it's low and high end ie, 5 and 9..but is best in between. Again, that's me with a theory though. Some food for thought if you will.
http://makingskincare.com/preservatives/