I don't have any MKIII listening experience, and I've not heard the K240, and I've not listened with the E7... Perhaps I'm the wrong guy to answer at all, but I'll add what I can about the LD I+
It does do well with low impedence headphones. I think it's a great performer for the money and I do beleive you'd notice a signifcant improvement of SQ by adding one downstream of your sound card.
55 ohms is on the low side, and from my experience the I+ hybrid design does do well with low impedence headphones. I would add though, that I've been pleasantly surprised at how the LD handles my Orthos's and high impedence cans. It may not be ideal, but it's quite versitile. There are some trade offs, for instance I find my the highs on my HD600's tend to get shrill and harsh, especially with certain tubes rolled in... but I've been really happy with how the HE-5LE's sound. Grado's love this little amp. My point it that you shouldn't think of the I+ as being a one headphone amp.
Op amp and tube rolling may seem intimidating at first, but it's really easy and it gives you the opportunity to fine tune the amp for the headphones, music, etc... you are using. Fun stuff, you can customize.
I'm sure others will have more information the other kit you asked about.