Lviv/Western Ukraine is also very anti-Russia and has been for a long time (pre-WW2). Ukraine is a very divided country and there is more than one opinion on what to do. If each region voted independently, you’d probably see Ukraine split into two states, one aligning with the EU and the other with Russia.
For what it's worth, the Party of Regions, which used to be in power until 2014 and which got voted into power by South and East of Ukraine, won the 2012 elections with a program featuring signing the Association Agreement with the EU, visa waiver with the EU and joining the EU market.
Anyhow, if the question "Would you rather be in a political and economic alliance with the EU or with Russia?" might have seemed divisive to some before 2014, I'd think Russian aggression fixed that for good.
Kharkiv, east of Ukraine.
In Ukraines case, do you really think they don't want to become more like any EU country? I know plenty of people from Lviv. That 'coup' was not staged by 'the west', but was a force within their own population that want a better standard of life.
So please don't compare US involvement in any Middle east country to the EU and their neighboring countries.