you have squeezed too much in your questions and made some premature assumptions. Not all travertine came into existence at the outlet of a hot spring. The term covers the wide range of rapid calcareous precipitation from ground water to surface water near the surface or in underground rooms be it a cave or along fault zones.
Although CaCO3 prevails, it is not the only mineral found in the afore-mentioned sites. Therefore Sr and Y are only part of the chemical budget and have to be considered together with other elements such as REE, Ba, Ca, Mg... which compete for the same sites in the lattice during site occupancy.
With kind regards
H.G.Dill
DILL, H.G., LUPPOLD F.-W., TECHMER, A. , CHAODUMRONG, P. and PHOONPHUN, S. (2004) Lithology, micropaleontology and chemical composition of calcareous rocks of Paleozoic through Cenozoic age (Surat Thani Province, central Peninsular Thailand): Implications concerning the environment of deposition and the economic material of limestones.-Journal for Asian Earth Sciences, 23: 63-89.
DILL, H.G., TECHMER, A., BOTZ, R. and WEBER, B. (2012) Chemical and mineralogical variations at the transition from subaqueous to subaerial rift-related freshwater limestones along the Dead-Sea-Transform Fault, NW Jordan.- Zeitschrift der deutschen Gesellschaft für Geowissenschaften, 163: 91-112.
These papers are available for download from the Researchgate Server.
Leyla Kalender and others 2015, Geochemistry of travertine deposits........,Turkish Journal of earth sciences, 24:607-626. full text and related references on line available.
While Sr/Y is a widely used geochemical indicator in igneous petrogenesis, its value as a discriminator of low temperature water-rock interactions has not been explored. Nor, to my knowledge, have Sr/Y systematics been established in studies of groundwater geochemistry. Groundwater anomalies in Eu, Ce and Y (and the Y/Ho ratio) have been used to relate groundwater reaction with particular lithotypes, but I am unsure of the extent to which such anomalies would be inherited by travertine or tufa precipitates.
However, there are several studies which attempt to link travertine trace-element, rare-earth-element and stable isotope characteristics directly to a dominant, putative ‘source’ lithology. I would particularly recommend you take a look at the paper by Teboul et. Al. (2016), which provides a comprehensive guide to previous work, while proposing potentially valuable geochemical indicators for travertine litho-sources based on δ13C - δ18O cross-plots, the barium–strontium cross-plot, absolute chromium abundance and absolute beryllium abundance.
Also check out the research in this area by Peter Moeller (Möller) of the Helmholtz-Centre Potsdam (example given below).
Hope this helps
Regards
Graham
Teboul, P-A., Christophe Durlet, E. C. Gaucher, A. Virgone, J-P. Girard, Julien Curie, Benjamin Lopez, and G. F. Camoin. "Origins of elements building travertine and tufa: New perspectives provided by isotopic and geochemical tracers." Sedimentary Geology 334 (2016): 97-114.
Möller, P. (2000). Rare earth elements and yttrium as geochemical indicators of the source of mineral and thermal waters. In Hydrogeology of crystalline rocks (pp. 227-246). Springer Netherlands.