Would just like to update that I'm finally on Windows 10.
Apparently the issue was with my boot file, the BCD and recovery. Had to rebuild my BCD. Then to make sure all is good I also added a recovery on my C drive and registered it. I don't know what Lenovo did but I had "one key recovery" that came installed with the laptop that never worked. So got rid of it earlier.
Anyway, just in case anyone faces a similar problem, Windows 10 update failing at 24% and getting the silly and very informative "Something went wrong" message, error 80070003, I'll leave the solution here
Note: Because I didn't have a working recovery, I couldn't reboot in recovery mode. So what I did is I booted into Windows 10 like I'd normally do to install, then click on repair, advanced settings, and open CMD from there. You cannot rebuild the BCD after you've booted into Windows obviously since the file's in use, so you'll have to do it after booting from recovery mode.
"I had exactly the same problem. Fixed it by rebuilding BCD - boot configuration data. You can find numerous tutorials on how to do that in the Internet. However keep in mind that the process is slightly different for EFCI boot mode and legacy boot mode.
Just in case, here is the instruction that I followed. It's for EFCI boot mode, for legacy boot mode there's a good one here.
(enter commands in command prompt in system recovery):
diskpart (opens Disk Partitioning tool)
select disk 0
list volume (please note the number of the volume that has no drive letter assigned and has FAT32 listed in Fscolumn)
select volume <the number of ~500 MB FAT32 volume with no drive letter, or with label ESP>
assign letter=Z: (gives drive letter Z: to EFI System Partition)
exit (closes Disk Partitioning tool)
cd /d Z:\EFI\Microsoft\Boot\ (changes current folder in Command Prompt window)
attrib Z:\EFI\Microsoft\Boot\BCD -h -r -s (removes hidden, read-only and system attributes from BCD folder)
ren Z:\EFI\Microsoft\Boot\BCD BCD.old (renames BCD folder to BCD.old)
bootrec /rebuildbcd (retries the rebuild)
Now, in the Add installation to boot list line, type Y and press ENTER. Now, it should say something like "completed successfully". The new BCD is ready, close Command Prompt and restart your computer."
Cifad's response in
http://answers.microsoft.com/en-us/...431a-b4e4-9ae12cfd89a2?page=~pagenum~#Windows.
Use this if you don't have a working recovery mode/image/disc to create a new one

Do this step
after you've rebuilt the BCD above.
http://www.makeuseof.com/tag/restore-deleted-recovery-partition-windows-8/
Hope this helps whoever's in need and great credit goes to Cifad from Microsoft's website.
I'd like to point out that these so called IT Support "Pros" are useless idiots who just parrot solutions without thinking.