A choice of cutting tool to be used for any machining operation depends on many factors especially those relating to the mechanical and thermal properties of the material, like hardness, YS, UTS, etc. Because Titanium is ordinarily a hard material, Dry machining machining is best suited (many publications in science direct, scopus etc. are available on machining Titanium).
PVD as made mentioned by Salvado above is a common choice for a cutting Insert but in addition you can use many other like coated ceramic tools etc. Normally, high speed machining is preferred, but generally, your objectives for the machining operation will guide your choice for the parameters to be used.
Sub-micronic straight tungsten carbide turning tools can be used to machine (turning) titanium alloys with copious application of cutting fluid (soluble oil).
If you have the facility for high-pressure cooling, then cutting speed can be enhanced substantially. Please refer to:
Article Some studies on high-pressure cooling in turning of Ti-6Al-4V
Article Effect of coolant pressure, nozzle diameter, impingemnt angl...