Microsoft seemingly confirmed that Rise of the Tomb Raider is getting a DirectX 12 patch. It's been rumored for some time so this statement makes it a bit more official:
DirectX 12 Showcase: Rise of the Tomb Raider, Ashes of the Singularity, King of Wushu – Square Enix, Snail, and Stardock showcased their latest DirectX 12 enhancements for Rise of the Tomb Raider, King of Wushu, and Ashes of the Singularity on Origin PCs, iBUYPOWER Revolt 2, and Maingear PCs. Ashes of the Singularity is taking advantage the DirectX 12 multi-adapter technology, allowing PCs to use multiple GPUs, even from different manufacturers. Rise of the Tomb Raider was playable for the first time at the Xbox Spring Showcase running DirectX 12.
It's unknown when gamers can expect the DX12 patch.