If you are using the current TurnKey v15.1 lamp appliance then that already comes with PHP 7.0. The previous major TurnKey version (v14.x) came with PHP 5.6.

Some have raised concern previously that PHP 7.0 is EOL by PHP upstream and is no longer supported. However, because TurnKey is based on Debian it will receive security updates direct from Debian (they are still supporting PHP 7.0 until the end of Debian 9/Stretch; by the Debian Security Team until 1 year after Debian 10/Buster release, after then it will pass to the Debian LTS team).

So if PHP 7.0 is acceptable for your purpose, then I recommend that you stick with that.

However, I note that a number of upstream PHP apps now require PHP 7.1+. So if that's the case you find yourself in, then those instructions you link to look good to me. We will be using a similar method to provide PHP 7.2 for a few of our appliances that will be updated shortly. FWIW the next release of NextCloud, ownCloud and Magento (to name the ones that spring to mind) will all include PHP from the deb.sury.org repos. FWIW the guy that maintains those is also on the PHP packaging teams for both Debian and Ubuntu, so they're a trustworthy source.

To explicitly answer your initial question though, TurnKey v16.0 will be based on the upcoming Debian 10/Buster. Buster includes PHP7.3 OOTB. Hopefully we'll be able to release v16.0 soon after Debian release Buster as stable. However, it almost certainly won't be immediate.