Of course it slows down the internet connection (can be applied to all VPN solutions): the CPU does not have enough performance to decrypt traffic on-the-fly.

There is another option: you internet carrier throttles VPN using DPI (but it less likely).

Anyway I’m still open for suggestions on my problem. The issue is that nslookup works fine (if I specify my custom DNS) server:

nslookup  test.lan 10.123.123.1
Server:   10.123.123.1
Address:  10.123.123.1#53

Name:      test.lan
Address 1: 192.168.77.1
*** Can't find test.lan: No answer

but with the default DNS it finds nothing:

nslookup test.lan
Server:   127.0.0.1
Address:  127.0.0.1#53

*** Can't find home.lan: No answer
*** Can't find home.lan: No answer