Hello raza.ajmi and everybody,
The grub.cfg in post #9 designates NTFS partitions in the fdisk reported in post #14. It never had a prayer of working, but it does serve to prove that raza.ajmi truly is mixed up about the partitions. I agree with that being a bad thing right about now.
I don't know why update-grub in Ubuntu is not working to generate a menu entry for LFS in the Ubuntu menu. Sorry. Another idea just for the time being is to emergency boot the LFS system from the Ubuntu GRUB menu grub prompt. I do this all the time for test systems not listed in any boot menu. It's quite easy and could at least let you move ahead for now. You can fix the main boot loader later when you understand the partitions (and GRUB) better.
If you want to try that, then press the "c" key when the Ubuntu GRUB menu appears. That will stop the boot countdown and present a grub> prompt. See the screenshot for the easy steps.
I don't use separate boot partitions. If you do, then don't use "/boot" in any of the paths in that example. The search command may find multiple grub.cfg files (e.g., Ubuntu's and maybe others). You have to know or figure out which is which (or try them all). You have to get the "root=" kernel parameter right or it will not boot. It's the device name (or LABEL, or UUID) of your root partition, and it has to be right.
Another idea is the Super GRUB 2 Disk (easy to find with Google). It's a CD that can boot your system (provided it is capable of booting). Besides, it a good thing for anybody to have around anyway.