The only way you will be able to work on raw image data in Lightroom 4 with that camera will be to use the final release DNG converter 8.7 when it is finally released. It is not available yet. When Lightroom 5.7 is released there will be support for that camera, but only from Lightroom 5.7 onward.
For right now, you will have to wait for the DNG converter 8.7 to be released. If you want full support for your raw files then you will have to upgrade to Lightroom 5, but wait for the next update.
As an interim solution, you can use the DPP software that came with the camera to create TIF copies of your raw files that you can use with Lightroom 4.4.
I understand you are frustrated like many other users. But before you start venting your frustrations and telling us how badly you NEED support for this camera, that is vital to your business, type your camera model into the search feature at the top of the forum. You will probably read every question and answer possible.
Thanks for the rely. Do you have a time scale for the release of 5.7 by any chance?
Soon, which has no specific time line. So maybe as soon as it meets the satisfaction of Adobe quality control.
Also be aware that the update will not only provide support for the EOS 7 Mk 11. All the intended updates and bug fixes have to pass the quality standard of Adobe.
Native Lightroom support for the D750 was added in the Lightroom 5.7 update released this evening.