OpenVPN client to use local DNS server and VPN provider's DNS server
Yes, I had tried the various dhcp-option, these leads nowehere. In the meanwhile I found a solution for macOS:
you create /etc/resolver/lan with the following content:
domain lan
nameserver 10.0.1.1 <- the local dns server
search_order 1
search lan <- important! otherwise you must append .lan every time by yourself
Now the system behaves exactly as I wanted. local machine names are resolved properly without the need to append ".lan", and external names get revsolved via the VPN provider's DNS server. There is no DNS leak.