I assume you know that a perfect skating lunge requires you touch the side of the boot, not the blade - which means the foot must be sideways - ideally rotated at the hip socket, like a Warrior II Yoga pose http://www.wikihow.com/Do-the-Warrior-II-Pose-in-Yoga
Except that a really nice skating lunge goes lower, and bends the knee more sharply than 90 degrees. (But! If you have a bad knee, ask your doctor about how much you can safely do! Deep knee bends can be bad for people with cartilage damage. I'm not sure if there is also a problem for people with ACL or PCL injuries, or muscle sprains.) Note that the picture at that link shows the back foot vertical, so the blade would touch - you have to go deeper to touch the side of the foot. https://images.nikonians.org/galleries/data/11817/medium/Colonial_comp_0408_lunge.jpg
(But with a smile, and don't look down! And touch as much of the side of the boot as you can, not just the front, if possible.)
There are lots of arm/back position variations, like http://2.bp.blogspot.com/-dVXRLVtOdDs/TpLg4mjGwQI/AAAAAAAADSA/gyCqww2AerM/s1600/Jeffrey_Buttle_2007_Skate_Canada.jpg
This probably doesn't help, but there is a gal at my rink who does very low sideways lunges during off-ice warm-up. When I try to go that low, I collapse. It requires real strength.
A typical (forwards-motion) skating lunge (which isn't sideways) is relatively easy for me, because it is at the limit of my flexibility, so I can't collapse. (Besides, I used to fence.) It would require more strength (tighten the muscles around your tummy) if I was super-flexible.
BTW, are you going as low as you can? - that might help, though I suppose you might not have the strength to come back up - and like I said, if you've a bad knee, ask a doctor. Also, if you have the flexibility to touch the back of your calf to your ankle, I think some people might think you were cheating.
A backwards-motion lunge is harder, because, for the same reasons, I often touch the blade instead of the side of the boot, so I jerk to a stop. I need to use all my strength (to extend that flexibility, and bend the ankle a bit) NOT to touch that blade. The blade isn't supposed to touch on a forwards-motion lunge either, but nothing terrible happens if it touches a little at first.
Because my current boots are suede, which is rough enough to have a lot of friction, I have to use boot covers to slide. (Which also prolongs boot finish.) Is your leather nice and smooth?
But your problem is much more likely balance, possibly exacerbated by insufficient lower abdominal strength (tummy muscles not tight enough). You could practice sliding in lunge position on a smooth floor and socks. But don't hurt yourself by bumping into kitchen counters.