Locking tuners are really designed for tremolo systems to be a non invasive alternative to a locknut or stringlock, thus keeping the original head stock intact and free of new holes...
It also keeps tuning stability and makes string changes easier. But in order to make tuning stability perfect, you need very slippery nut slots, or the strings will catch when bending the strings and your guitar tuning wont return to pitch. Locking tuners with a Teflon nut can be used in place of those unsightly stringlocks, if you want to keep your axe as original as possible. In order for locking tuners to work properly, your guitar or bass must have a specific type of configuration to it, or it's simply not going to be stable enough for tremolo work.
The best configuration you can have for any locking tuners is a head stock with inline tuners like a Fender Stratocaster or a Fender Precision/ Jazz bass has. On these type of head stocks, the tuners are all in a straight line configuration. All the strings will go straight thru the lubricated nut into the tuners without any real bends (a slight down bend from the nut to the tuners is OK and is proper).
The worst situation for locking tuners by themselves is any 3x3 tuner configurations such as Gibson Les Paul's where some strings veer left and some veer right after exiting the nut. When you tremolo or bend deeply, the winding on the strings will always stick to the outside corners of the nut. Grooves will develop in the nut slots over time. These types must use a stringlock or locknut to keep in tune.
Most hockey stick type head stocks like Gibson Explorers or the pointy type Jackson's have, are not a good match at all for a locking tuner and nut setup where the small E string veers downward, across the head stock span to the small e tuner at a sharp angle. Only use a locknut in this situation. However, Gibson V's and PRS guitars with 3x3's are OK, and are about the only guitars that comes to mind at the time of this writing that will work with locking tuners and self lubricating nuts because the strings go straight thru the nut and into the tuners the same as a Stratocaster does, only in a different design. See the pattern here? Inline Ibanez guitars such as the "RG" or "Jem" series are another perfect situation for locking tuners as well as all older "maple necked", inline head stock Peaveys such as T-60's, Predators and the Mantis etc...
I always recommend a self-lubricating Teflon nut such as the Black Tusq XL by Graph tech which is much less expensive or invasive to install and which i highly recommend. A couple of my axes have locking tuners and this Teflon nut setup. I love them because it keeps the original looks to the guitars.
I've been doing the tremolo gig since 1984 and I know from experience that a tremolo system is a very simple thing really. Two forces off-setting each other equally until you upset the balance with a Whammy bar. To work perfectly/properly, string ends must be locked tight and all strings must slide absolutely freely over all obstacles during dives and pull ups (obstacles like bridge rollers and nut slots).