Is it possible to link one single LN node to Bitcoin addresses? In René Pickhardt's presentation (slide 166) (here is the interesting talk), it's written that on-chain funds and addresses can be linked to LN nodes. How can this be achieved?

From my understanding, it is possible to link funds of a channel to two LN nodes, but it's not possible to tell which node funded the channel and how the funds get split among nodes in the settlement transaction.
If a channel is announced a multisig output - which encodes the capacity of a channel - is linked to two nodes on the lightning network. This mutltisig output is obviously onchain and can be seen as onchain funds. 

This does not mean that we know directly who funded the channel and how the funds are split between nodes in the commitment / settlement transaction. 

However the funding transaction was consuming some other outputs. They might have come from the settlement transaction of another channel. This links two funding transactions. The node that takes part in both payment channels is the one who funded the second channel. Currently lightning nodes reuse outputs and do not mix / coinjoin them. Thus the analysis is rather straight forward. 

However it seems that if nodes never reuse outputs and if channels never close it will be much harder to link funds to a single node.