The Lyr is not going to magically enhance the low end because most amps should be transparent. That means that your headphones are providing the second biggest bias to the sound signature next to the actual music. That said the K701 are always going to sound weak in the bass because they are just that...weak in the bass. The Q701 has been tuned to give a slight bass boost which can help, but for me it was going to something like the AH-D2000 to get the low end I expected from my gear. If you want more bass, and this goes for just about anyone out there, first change your headphones/speakers.
Take the HD-650 for example. So many of us have tried to change our gear to enhance the sound of the HD-650, but in the end the HD-650 dominates the sound signature of any setup because the actual speaker drivers are what is making the sound. Changing the signal prior to the driver will not physically change the shape and dynamics of the drivers so no major changes in the sound signature should ever be expected. Distortion is another thing, but expected the a huge difference is the sound signature by changing the gear prior to the headphone is going to almost always lead to disappointment. If you want more bass extension either slightly EQ there say at 40 Hz and 90 Hz +2dB and hope for no distortion or simply change your headphones. For many of us having two sets of headphones around for listening is key. One headphone will have a slight bass emphasis and the other will be more neutral with some peaks in the treble. By having two headphones you can cover 80 % or more of what most people listen to and not have to worry about not getting the sound you want.
The charts below list the K701,Q701, and D2000 and their corresponding frequency responses.
http://graphs.headphone.com/graphCompare.php?graphType=0&graphID[]=2931&graphID[]=703&graphID[]=2881
That should give you a general idea of what to look for in a headphone. Pay special attention to frequencies below 100 Hz and make sure that the headphones you are looking at have at least a +2dB bump over the K701 curve.
If you really like AKG and I can certainly see why you may want to look at the AKG K550. Other than some minor comfort issues with the headband they sound really good. Below are additional charts with the AKG K550 added. With a little extra padding around the sharp edges of the K550 you should have yourself a sweat pair of slightly more bassy headphones that will sound good with just about any type of music. Keep in mind they are not bass heavy, just more extended than the K701 you are used to hearing.
K550 Added Charts:
http://graphs.headphone.com/graphCompare.php?graphType=0&graphID[]=2931&graphID[]=703&graphID[]=2881&graphID[]=3571
You can get them here:
http://www.headphone.com/headphones/akg-k-550.php