After installing Trisquel 7 dual boot with Ubuntu , Grub is asking for password to boot Ubuntu

I had this happen years back with a Windows partition (I was young and foolish!). I recall it was a big with GRUB and one that cannot be fixed without installing a newer version from somewhere.

That said, you should do like I did and take it as a sign that you should stay clear of that non-free mess that is Ubuntu.

The user is "grub" and the password was randomly generated when Trisquel was installed. You can read it (from Trisquel) at the very end of /etc/grub.d/01_PASSWORD. Instead of learning that password, I suggest you to get rid of it... since it "only serve[s] to make it difficult to recover broken systems". That is what the developers of GRUB say:

By default, the boot loader interface is accessible to anyone with physical access to the console: anyone can select and edit any menu entry, and anyone can get direct access to a GRUB shell prompt. For most systems, this is reasonable since anyone with direct physical access has a variety of other ways to gain full access, and requiring authentication at the boot loader level would only serve to make it difficult to recover broken systems.
https://www.gnu.org/software/grub/manual/grub.html#Security

1. Open a terminal (emulator).
2. Open /etc/grub.d/01_PASSWORD (what requires administrative rights) with your favorite text editor (here GEdit):
   $ gksu gedit /etc/grub.d/01_PASSWORD
3. Add the "#" character at the beginning of all lines that do not already start with this character (or even delete these lines).
4. Save the modifications.
5. Make the configuration change be taken into consideration:
   $ sudo update-grub

I really hope this user-unfriendly GRUB behaviour is fixed in Trisquel 8.