Recovering Ubuntu after filesystem was overwritten using dd

I had an Ubuntu installation on my laptop, on an encrypted LVM (this was /dev/sda1).

I was planning to write an Arch Linux image to my USB drive (/dev/sdc1), following this guide - https://wiki.archlinux.org/index.php/USB_Installation_Media#Overwrite_the_USB_drive. Instead, I accidentally overwrote my Ubuntu by using

dd if=archlinux.iso of=/dev/sda

Is there any hope of recovering my Ubuntu installation, or is it totally hopeless, and I rather recover as much data as possible?

I'm assuming this is dm-crypt/ LUKS. How late did you realize this mistake and terminate the dd? If you've overwritten the salt in the header, it's impossible to recover your data. Otherwise, there are some tools in the cryptsetup-luks package to perform surgeries by hand and recover data. For more, see the questions that follow "What happens if I overwrite the start of a LUKS partition or damage the LUKS header or key-slots?" in the official LUKS FAQ.