I think everyone can relate to the idea of failure and the difficulties a person has to face in order to deal with failure.
Willy isn't a liar as much as he is a coward, too afraid to directly address the central issue in his life which has everything to do with success/failure and status.
Relating to Willy (and to the situation he creates in his family) is easy to do, I think, because we all have doubts, we all have dreams, and we all end up somewhere in between.
The ideal of striving for unattainable success is an ideal which has been taken up by many nations, although I do see that the Dream began as an American one. I found studying the play in 1980's UK disturbing in the the idea that the halcyon days would one day be gone - if they were ever there in the first place.
By the 1990's I saw my own father be made redundant twice to be replaced by younger, better trained, cheaper workers. The play certainly feels deeply relevant to my own observations of life in the UK - a different time and a different place.
You've got a great answer in post #1, but here are a couple more issues to consider: Losing face (honor, self-respect, respect of others in the community), success or failure in life, being satisfied with yourself as a person, the ability to support your family, and gender issues are all also universal appeals in this story. All of these things are not specific to just one continent or country, but they are central to Willy Loman's life.
While it's true that Death of a Salesman is centered around several themes which are primarily American in nature, such as the pursuit (and disappointment/failure) of the American Dream, there are also some universal experiences:
- A complicated relationship between father and son(s)
- Lack of loyalty and faithfulness (both business and personal)
- Growing old
- Keeping up pretenses out of shame, embarrassment, and denial
- Problems caused by lack of communication.
There are plenty of others, of course, but these are clearly not elements and experiences which are exclusive to the citizens of one country.