I'm sure you have, but just to begin from the beginning...
From the home screen menu>settings>security>change screen lock. You'll be prompted to enter your existing pattern for access, then choose 'none' if you want none or one of the others if you've changed your mind. Unselecting visible lock pattern will only keep the lines from being seen.
If this does not end the need for a pattern to unlock the phone have you installed any third party lock apps? I used one for our old phones to stop the kids from accessing things that may cost us money or affect the settings of the phone. It would also act as a substitute device lock if I had set it for that.
If you've tried all this before, and you're sure your device is not a corp. device that requires security, the last two suggestions I have are to try a battery and/or sim pull. If you still don't get the result you want, you may have to try a factory reset. If you end up going all the way with the factory reset you should probably also get a back up app, like MyBackUp Pro. It offers a trial period so you don't have to buy it, but it is a nice app to buy if you're really worried about getting everything back on the phone just the way it was. It won't save any app data unless you're rooted but it will put your homescreens back to how they were before and most of your phone settings. A cheaper way to go is to install Astro file manager. It offers the app and folder back ups, but not home screen or messaging back ups. Most third party texting apps will have a backup function built in, not sure if stock does? Anyway, just be sure whatever you back up is backed up to your external sd, and be sure not to select clear all memory when factory resetting. Internal sd would likely not be affected if you don't choose it but as an added safety, just for myself, I always put it on the external sd.
