OK well the best thing is that you know what you need to do, :o) your horse is short striding (not reaching under) not only in the lope but also in the walk and trot as well it just shows up more in the lope because he is unbalanced and keeps falling forward and like us when we first learn to walk when we loose balance we have to scramble forward to try and stay balanced.
The main reason for this unbalanced short striding in your horse I believe is lack of balance and to be properly balanced where the horse can move with energy and cadence they need to be strong through the top line and abdomen.
In order for us to be able to exercise the horses top line they have to accept our hands and legs and in order to get our horses to accept our hands and legs we have to be effective enough riders to ride in rhythm and deliver cues to our horses with in that rhythm.
I am including links to some video's that will show you how I go about getting my horses to accept my hands and legs and also how I start to develop the horses muscles so they can perform with a round frame and stay balanced.
If you like you can also go read my blog where I discuss many issues like yours and offer idea's for solutions. It is best if you watch theses video's in order and also you may know most of it but I wanted to start at the beginning so we did not miss any steps. :o) good luck and BTW you seem to have a nice soft set of hands and a good seat with practice this will all be easy for you.
And my blog Rod Miller IPHDA & NRHA Professional