All the feedback that L- has received about you has been completely positive. Near as we can tell, they literally love you out there. If anything, the only way your contract would be ending would be because they hired you as a perm FTE.
I will assuredly double-check with L- that your position there is completely secure.
But the short answer to your questions is: No, you really do not need to be looking for another position. Unless you are suddenly dissatisfied with their environment there, then the feedback we are receiving about you is that you can stay more or less indefinitely (certainly for the foreseeable near term), either as a contractor or a perm FTE. That method of employment distinction (TEK vs Perm ) sounded to us like it was the only part that was up in the air. Them wanting you to stay was not in question at all.
So, I will double-back with L- about all this again for you, just to be on the ultra-safe side, but you should not be worried at all, as least not according to all of the feedback we have from them about you and their future plans for you there.
Please definitely let me know your thoughts if you had any concerns about your position there, outside of the arbitrary 6-month mark designation that gave you any tribulation. They are telling us you are going steady, so unless you think there is anything else occurring, you are set with no worries going forward there.
* We should set up a time to connect for lunch again soon as well. I have Mon and Tues the 26th and 27th of Nov open, if either of those work for you?
J-