This paper analyzes the dynamics of U.S. lithium mining companies, the lithium industry and West Texas Intermediate (WTI) crude oil prices using a Fractional Cointegration Vector AutoRegressive model (FCVAR model) and a Continuous Wavelet Transform (CWT) for its resolution. The results indicate evidence of a negative relationship between FMC Corp with Albermale and SQM stock prices. These results are similar if we analyze the risk based on the beta term structure of each company. Analyzing the fractional differencing parameter for the stock prices and their logs, we observe that they are very persistent, and there are no long-term deviations in the stock prices. The same happens when analyzing the beta term structure. Based on Continuous Wavelet Transform (CWT) methods, our results show that lithium mining companies and the lithium industry are weakly correlated with WTI crude oil prices at higher frequencies (short-run) and persist through the sample period. At lower frequencies (long-term) the time series reached a high level of dependence between late 2012 to mid 2016, concluding that the lithium mining companies and the lithium industry reflect and foreshadow the responsiveness of the WTI crude oil prices during the period mentioned above.