There will be people in poverty when they spend their basic income checks on drugs...
You're confusing two things together. There are drug addicts who have to be saved by means in addition to financial means for basic necessities. But the majority of poor people aren't like that. It's not to say poverty can be totally eliminated, but it will be massively improved upon at the very least.
Basic income would not lift people out of poverty.
What's the very definition of "poverty"? Having no money for even the basic necessities. By its very definition, basic income deals with that. Surely there are drug addicts etc. who would just be fucked no matter whether they have money or not. But if you genuinely believe that every poor man is like that, you're way too brainwashed by the rightist elitist BS justifications for their own wealth, my friend.