Do sins such as bearing false witness prevent the payment of the expiation for a vow or the expiation for delaying a vow before expiating these sins?

There is no connection between offering expiation for a vow and repentance from bearing false witness. Repentance is immediately obligatory. It is permissible to pay what is due from the vow before repenting, while emphasizing the prohibition of false witness and the necessity of repenting from it.