Here is a good write up on Y (ADR) share vs F share (U.S....

Here is a good write up on Y (ADR) share vs F share (U.S. Over-The-Counter (OTC) Foreign Ordinaries). Their benefit and risk. The table in there sum them up.
https://www.schwab.com/stocks/understand-stocks/adrs-foreign-ordinaries-canadian-stocks

Depending on whether you trade often in-and-out or not, and hold long or not, Y share has ongoing management expenses (custody fees and fees for processing dividends and corporate actions) while F share has higher trading commission but no fee.
Liquidity is low for both, for example today LYSDY trading volume is 375,952 while LYSCF is 639,568. For Lynas, I usually see twice the trading volume on LYSCF compare to LYSDY. The F share has no US bank involve as middleman, just go through the exchange, OTC, and trade directly. I personally like that better.
I hold a lot of LYSDF. Over a year ago I called my broker Fidelity to convert some to the ASX share LYC:AU and they converted right over one-to-one with a phone call. No problem. Since then I have exposure to the trading hour on both exchanges. With that, I think it should be as easily convertible to US NASDAQ shares if it gets listed there.