I am not sure whether I understand your problem correctly, but if you are interested in similarity of subsequences, take a look at LCSS measure
TSlearn package with an example:
Main idea is that LCSS is looking for Longest Common SubSequence in time series. As you are familiar with DTW there is a nice comparison between these two similarity measures in the image below (given as an example in the science article listed in references). LCSS is not taking into consideration outliers or different continuations after the subsequence between the two time series are met.
Also there is no assumption that a set of values (subsequence) needs to be ordered.
Also, LCSS is connecting the subsequences on different indexes. When you will be trying out this measure, do not forget to tune the parameter epsilon, how far it is acceptable to look for similar values. (f.e. in list_2 there is '4' on index 4, and in list_1 there is similar value on index 10)
M. Vlachos, D. Gunopoulos, and G. Kollios. 2002. “Discovering Similar Multidimensional Trajectories”, In Proceedings of the 18th International Conference on Data Engineering (ICDE ‘02). IEEE Computer Society, USA, 673.