I am not sure about MacOS, but in Windows, you can assign each interface a priority. The DNS server for the interface with the highest priority is used for all lookups. When you connect to SNX, it promotes the metric of that adapter (routing your DNS requests through the new CheckPoint Virtual Network adapter) to 1, but keeps the other connections at a higher value (e.g. 25, but you can check that by listing the routing table on the host).
If you want to use the DNS server on the LAN whilst connected to SNX, you could either promote that interface by giving it a lower metric, or you could manually configure the SNX Virtual Network Adapter to use your DNS server.
If you want to resolve your DNS selectively (based on target domain), you could use a DNS intercept tool, which intercepts DNS queries at the system level, and directs them to the appropriate DNS servers based on a set of predefined rules. I think on MAC, you may even be able to use DNSMASQ.