Removing left-recursion in grammar while maintaining left-association of operator
Compatibility of left associativity and LL(1) parsing

You just hit one of the major inconsistencies in the use of
context-free (CF) syntax. People want to choose grammars so that the
parse-tree will reflect the intended structure of the sentence,  close to its semantics, especially in the case
of non associative operators, such as application. This was pretty much the original intent of CF grammars in linguistics. But at the same
time they are constraining themselves to parsing technology that will
tolerate only some types of grammars.

Indeed, if the parse-tree is to reflect the left associativity of an
operator, then the grammar is necessarily left-recursive, since the
top application node in the parse-tree is necessarily adding the
rightmost term of non-parethesized successive applications.. So LL
parsing is out of the question. You are right.

There are two ways out of this. One is not to rely on the parser to
give the rigth "parse-tree" to be used for later stages of processing
(such as reducing the lambda expression, here). This lead to the
concept of Abstract Syntax Trees (AST) that can be built from the
parse-tree, but with a different structure.

The other solution is to use more general parsing Techniques that will
accept any CF grammar, and parse in accordance with it. General CF
parsers is a well developed technology  (and I do not cease to wonder
why LL remains so popular).

I have no idea what could be considered a proper answer to these
contradicting requirements.

What I would do is show they are contradicting requirements. Give a
first grammar that meets the associativity and priority constraints,
then transform the grammar into and LL(1) grammar for the parsing.

The fact that something appeared in a journal or on an exam is not a
total garantee that it is correct.  And I might be wrong too ... but I
did some checking, in addition to my own knowledge of the issue.

About this specific example

This being said, the first grammar you are suggesting does not seem
quite correct. It does not have a way of producing λu.λv.v .

One trick to know is to start with operators (here abstraction or
application) with the lowest priority (abstraction). It is the same for arithmetic
expressions.