Not knowing how Lyft/Uber service is on the area you are staying, and seeing that the hotel does not provide shuttle service, here are some suggestions that I will offer.
1) Look if public transportation is an option, and something that you are comfortable with
2) With ride share, its a gamble, I will allow myself at least a 3 hour window to get to to airport, after taking all the check in, security, etc. in consideration
3) Check with front desk to see if they have some type of unscheduled service to airport, perhaps offer to pay