In Expression Language you can just use the == or eq operator to compare object values. Behind the scenes they will actually use the Object#equals(). This way is done so, because until with the current EL 2.1 version you cannot invoke methods with other signatures than standard getter (and setter) methods (in the upcoming EL 2.2 it would be possible).
And you need to make sure that the entire expression is placed inside the same ${...} scope. Anything outside that is not interpreted as part of an EL expression.
So the particular line
<c:when test="${lang}.equals(${pageLang})">
should be written as (note that the whole expression is inside the { and })
<c:when test="${lang == pageLang}">
or, equivalently
<c:when test="${lang eq pageLang}">
Both are behind the scenes roughly interpreted as
jspContext.findAttribute("lang").equals(jspContext.findAttribute("pageLang"))
If you want to compare constant String values, then you need to quote it
<c:when test="${lang == 'en'}">
or, equivalently
<c:when test="${lang eq 'en'}">
which is behind the scenes roughly interpreted as
jspContext.findAttribute("lang").equals("en")