Well said, Maria. Definitely answers the original question! I have been a Loews First member since 2001 and one of the benefits, indeed, is a free upgrade (in this case a better view room) when available. My favorite benefit is the cookies and milk at check-in, but I digress 
Maria is 100% correct, you must mention you are a Loews First Member and inquire about the upgrade. Since they put this blatantly on their website, I do not think anyone at the front desk would internally berate you for this since it is part of the program. A club level is unlikely if you are a new member, but you could very well get a better view.
If you are not yet a Loews First Member, you can simply sign up on their website ahead of time. They will send you a card in the mail. If you do not receive it before your trip, simply bring the ID number they assign you. When filling out the form, you can also indicate what types of pillows, what newspaper, and what check-in "perk" you prefer (cookies & milk, water, and there might be something about fruit - I can't remember...).
I hope you get your upgrade and have a wonderful trip!

Maria is 100% correct, you must mention you are a Loews First Member and inquire about the upgrade. Since they put this blatantly on their website, I do not think anyone at the front desk would internally berate you for this since it is part of the program. A club level is unlikely if you are a new member, but you could very well get a better view.
If you are not yet a Loews First Member, you can simply sign up on their website ahead of time. They will send you a card in the mail. If you do not receive it before your trip, simply bring the ID number they assign you. When filling out the form, you can also indicate what types of pillows, what newspaper, and what check-in "perk" you prefer (cookies & milk, water, and there might be something about fruit - I can't remember...).
I hope you get your upgrade and have a wonderful trip!