Well, before I let the myself ramble on this, I know it'll be long. I love these and hate them at the same time.
I reckon its one of the most difficult exercises to learn and coach, except for those who just nail it instantly but they are few and far between.
I think they are a great exercise when performed correctly. The hip stability you need to control the knee when the other leg is unsupported is one "healthy" advantage. In movement terms there's a whole lot going on, you need hip flexion in one side whilst extending the other, all whilst keeping a neutral spine and not falling over. Remember it's really just a one-legged-hip-hinge and we all could do with more hip hinging. Beyond that it's just a good posterior chain exercise and you can actually train these pretty intensely when you have mastered form, however for some people form almost seems like a never ending battle.
Anyway, you shouldn't feel it in your lower back. You should feel like you're drawing back the hamstrings then releasing/pinging them forward, finishing with the glutes, and the lower back should just go along for the ride, not changing position and just transferring force. Also, when you get them right, you will feel the hamstrings loading quite significantly even with just body weight. The eccentric should more or less feel like a hamstring stretch on the working leg.
The most common issues I see are:
1. Bending at the back, not hinging at the hips
2. Externally rotating the hip of the rear/elevated leg. Basically, you twist as you go down. I',m not sure if this is hip external rotation, or a "collapse" of the other hip into internal rotation, it's a chicken and egg thing, really. Either way, you see the back toe rotate out to the side.
For number one, you will also see a major disconnect between the torso and the rear leg. So, from the side, the rear leg and the torso will form a kind of, triangle (i didn't want to say pyramid

) with the a$$ being the highest point. You don't want this. Sometimes in this position, the spine will flex but not always, sometimes it's still pretty flat but you still have a major disconnect.
You should imagine a big metal pole has been stabbed into your shoulder and down into the elevated/rear leg, all the way down to the foot (I genuinely use this description with clients) - in other words, move them together. Begin the movement with the rear leg - lead with it. The rear leg is very important. Begin by shoving it back and let the torso follow - when the rear leg "runs out" of extension, assuming you have a tight torso (scap down), you will naturally go and hinge/flex at the other hip, and this is when you should feel that hamstring stretch. Sometimes this really cleans up when I cue starting with a tall posture, and thinking of pulling the *scap "down", then swinging the leg back and letting the body follows.
*scap down really means, "switch on the lats" - it's all in the lats, especially when it comes to the core. The lats connect your shoulders to your hips, if you have the lats fired up in a tall posture, it's actually quite difficult to flex the spine. I actually just say "shoulder blades" or just, "shoulders" to clients and they know I mean, "pull them into your back pockets".
So, get tall, get tight (Lats!), lead with the rear leg. Find the hamstring stretch on the planted leg on the way down. Also, with the rear/elevated leg, as you move down, really "reach" with it, reach way back into the wall behind you. If you take anything away from this, take the "reaching" cue.
Number 2, externally rotating, is quite literally a pain in the a$$. Some people it cleans up simply by telling them to point the toe in the opposite direction, so if it's the left leg swinging backwards which is the problem and therefore, the left toes will start to point out to the left (if you were the person doing it), then you begin by pointing the toes to the right/internally rotating the hip, then you do the movement. It'll normally make you really shaky at first but after a few attempts it gets better and eventually, you don't need to point the toes any more, you'll just be able to do it.
I've not been able to turn everyone into a perfect single leg deadlifter, though, there are a couple of clients that are very difficult. I have very long winded theories that I don't quite understand yet. Anyway, the above is kind of rushed and all over the place, obviously I don't know what's going wrong when you try it so can't give specific cues but, hopefully there's something there you haven't thought about.
KPj