Lachy and Przyrowie is offensive.
Quite an interesting phenomenon. In 17 century Lach was the only term in Russian for Roman Catholic szlachtic from the Crown. Sometimes Russians called Roman Catholics from Litwa also az Lachy. That was quite neutral and the only term for Poles.
Now it may be derrogatory in Russian but not in all cases (for example for Russian historian it is quite neutral and historical). As to its derrogatory sense now, it in my opinion came from West Ukraine. It could be also neutra there but some old west Ukranians hated all Poles since Austrian period.
As to Russians they seem to know nothing of derrogative names of Poles. Sometimes the expression Pszek is used but very few Russians know it (I learned it first when I was 42 years old from a Polish article). That occures because Russian man in the street knows very little about Poles and doesn't have contacts with them at all and Rissian mass media inform only about meal problem and few Polish activities in EU. As to antimissil challenge, it is described as complete USA creation. You see, no possibility to invent any derrogative name