If you feel that you are genuinely in danger of persecution or fear for your life then you should consider seeking asylum. IF things are really that awful in Libya then the country you apply for Asylum in should be responsive to that.
But you need to do your research, and I mean really do it. I have no idea where you've been thinking of seeking asylum, but there's no guarantee that a country will grant you anything if you use things like your homosexuality as the reason as to why you wish to flee (it's a terrible shame that people need to use their own sexuality as an excuse in the 21st century).
Only recently a woman idetifying as LGBT was deported from the UK back to Uganda where she faces almost certain persecution and possibly even murder owing to that state's very extreme anti-homosexuality laws and anti-homosexuality sentiments:
http://rationalist.org.uk/articles/4632/...nd-nigeria
So do your research, and ensure your case is watertight if you're genuinely thinking of fleeing. Also consider that sentiments towards asylum seekers (at least in my own country, England) are generally negative, and the system you'll go through for your application will be draconian. Money granted to AS's here in the UK has been reduced drastically, and the accommodation you could be put up in could be very sub-standard:
http://www.refugeecouncil.org.uk/policy_...m_-_page_1
There's even been evidence of homosexual AS's being asked to prove their homosexuality:
http://www.bbc.co.uk/news/uk-politics-24479812
You need to bare in mind if, for example, you came over to the UK as an AS, the money you'd receive would not go far. The cost of living here is extremely high, and the benefits you'd be entitled to, be it welfare or even the opportunity to work, would be extremely limited. It's extremely unfair and based (IMHO) on hysteria about migrants coming to the UK to get money and nothing else. But it's the system you'd be confronted with.
To my knowledge, unfortunately, the systems around most of Europe are not much better.