It's definitely possible to get a loan as a foreigner but the rates will be high(er) and the downpayment required will be as well.

What is the interest rate on the HELOC?

Potentially lower down needed of 15% with better rate and 6% cap in IPC’s

For a cash out refi, you are generally limited to 75% LTV and rates right now are in the mid 7s for good credit and a DSCR over 1.0. 

A great lake front home doesn't have to cost a mint but it sounds like you want something that is really fantastic which will bring a higher nightly rate.

Quote from @Sean Kirk: I'm seeing what seems to be 10%+ cap rates on roofstock.

Based on what you've told us, your rate should be at prime (7.5%), unless you are over 80% LTV, then it would be prime +1.Jeff

AirDNA shows it on the rise in terms of annual revenue, occupancy rate, average daily rate and revpar, with about 3,000 total listings.

It's an estimated cash on cash return given current rental rates subtract expenses assuming 7% interest rate, 10% management fee, 5% repairs, 5% capex and other expenses like mortgage, insurance, tax. it's a estimate to tell you what properties to analyze vs ignoreyou can see the are pockets of negative returns as well as pockets of positive return. this is to supplement the data @Devin Conley provided

That worked well when rates were 3.5% but that "strategy" no longer exists.