Is it possible to play ARK with two PS4 on LAN?

All the details about general online play requirements can be found at this help page from Sony.

Only free-to-play games can be played online without a PS+ subscription. Otherwise, at least one account in the console must have a subscription to PS+, and that account must have that playstation marked as its primary console in order for online play to be enabled in that console. As long as you have that, all other accounts in the console will be able to play online even if they don't have a subscription.

I have done some fiddling with both a PS4 and a PS4 pro, and I believe the PS+ subscription check is done online when the system boots. Failure to connect to PSN marks seems to disable online play until PSN can be reached again.

So to summarize: you can hook two playstations in a LAN for the smallest latency possible between them, but that's the only advantage you get. You still need at least two PS+ subscriptions to play online, and must be able to connect to PSN anyway. The only exception is if the games you wish to play are free-to-play.

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Since you are asking specifically about Ark, you should also check that game's page at the Playstation Store if you bought it online, or the game's case if you have the physical copy. In both cases you will find this:

Online multiplayer (2-70 players). A paid-for PlayStation Plus membership is required.

And later on:

One-time license fee for play on account’s designated primary PS4™ system and other PS4™ systems when signed in with that account.