Supporting this idea of LTC following BTC price is the halvings; LTC is one halving cycle (4 years) behind BTC. BTC block reward currently is 6,25, while LTC block reward is 12,5. Next LTC halving will come around august of 2023, when the block reward changes to 6,25.
If we apply the stock to flow -model popularized by PlanB, this behaviour of LTC following bitcoin with 4 year (one halving cycle) delay makes complete sense!
tl;dr: buying LTC now is like buying BTC in 2017 before bullrun.