Are homosexuals/lesbians not allowed in some hotels?

What? I think you're misunderstanding.

It was probably trying to make it gay friendly. Otherwise, it wouldnt use such a happy picture like a rainbow coloured house.

There's gay-friendly hotels that attempt to appeal to homosexual cliental.

My mums friend runs quite a large hotel in Auckland, New Zealand and I saw her buying quite alot of gay magazines because she wanted to make it 'gay friendly' because homosexuals have the largest amount of money to spend on leisure, demographically.

They were likely advertising that their hotel was gay friendly. Essentially, they're saying that gay people don't have to worry about getting a dirty look from the desk clerk when they check in with their partner, or have to hear snide remarks from the staff when they think they're out of earshot, or told not to hold hands while walking in the hallway because it might offend other patrons. They're simply emphasizing that they try to treat their gay patrons with the same dignity and respect that they would any other.

Hotel owners can be discriminatory, but I'm sure this is mostly a problem when it's a small hotel. For example in the south, some owners might turn away black customers. you don't have to tell anyone that you're gay or that your partner is sharing the room with you. But if you're in a homophobic area, it's a good idea to be discrete.

I doubt a hotel has the right to not let any gay people stay there unless its a country which is completely controlled by religion.

In something like half the United States, it is legal to discriminate based on sexual orientation. While likely the "gay" means gay-friendly or gay-owned, it is completely legal to refuse service to you in many places for no reason other than your actual or perceived sexual orientation.

Yes they we're trying to advertise that they are Gay friendly. According to state and federal laws in the US, it is illegal to deny someone housing (including hotels) based on their orientation.

it means gay friendly. the others allow gay people but this one is more for gay couples go or have conventions at or something like that

I'm pretty sure that refusing service to people solely based on their sexuality or sexual activity or association with another person regarding sexuality or sexual activity is illegal in Australia.

A business can deny service to anyone for any reason except their color. Depends on how Conservative the owners are.

Where?

They're not allowed to discriminate in the UK or they get fined. In some countries I'm sure they can and do discriminate.