If dark matter is dissipationless and only interacts gravitationally, then no it can't. How could it be brought to approximate rest$^1$ with respect to a Lagrangian point, its inertia would mean it just carried on with whatever kinetic energy it had?
If dark matter is weakly interacting then it might be possible for it to accumulate in deep gravitational wells formed by ultra-dense matter - i.e. in white dwarfs or neutron stars. But such ultra-dense matter does not exist at Lagrangian points in the Solar System.
$^1$ Something "at Lagrangian points" (the wording of the question) is necessarily at rest on average with respect to those Lagrangian points. They are actually effectively in orbit around the more massive body. There is no mechanism to decelerate and capture dark matter into an orbit with a speed of $\sim 30$ km/s (e.g. for an orbit near Earth) when dark matter is travelling past the Sun with typical speeds of hundreds of km/s.
Even should one argue that the dark matter has a distribution of speeds and some of it will be travelling at close to zero velocity with respect to the Sun, that matter will be accelerated towards the Sun as it approaches and would stil not be captured at the Lagrangian points.