When moving a unique_ptr into a lambda, why is it not possible to call reset?

1. Why does this happen?

Because the function-call operator of a lambda,

Unless the keyword mutable was used in the lambda-expression, the function-call operator is const-qualified and the objects that were captured by copy are non-modifiable from inside this operator().

and

2. Is it possible to capture the std::unique_ptr in another way which allows to call reset() within the lambda

You need to mark it mutable.

mutable: allows body to modify the parameters captured by copy, and to call their non-const member functions

e.g.

auto l = [v = std::move(u)]() mutable {
    v.reset();
};