Liz is owned by Walgreens/Boots(well technically just Walgreens a US company who own Boots) now.
The three mentioned sell to China who insist on testing, so that means even if the company does not test in US and EU their products will be tested in China(the weird part is products made in China for sale outside there are not tested). So some will refuse to buy these brands and others won't. EL owns so many other brands how far you want to go is up to you. An example is Smashbox, they had the bunnylogo(US version of the symbol which is a bunny head with big ears), they were bought out by EL and lost their bunny as the brand was then sold in China. Aveda now owned by EL never had the bunny but was considered by many to be ethical.