I guess hope can be false now.

Sure, if by "now" you mean "at least since Geoffrey Chaucer's time":

> And thys vyce cometh of false hope that he thynketh he thall lyue longe, but that hope fayleth ful ofte.

[1] https://www.google.com/books/edition/The_Workes_of_Geffray_C... [2] https://books.google.com/ngrams/graph?content=false+hope&yea...

Or, come to that, "at least since Cicero's time":

> ...cui legi cum vestra dignitas vehementer adversetur, istius spes falsa et insignis impudentia maxime suffragatur.

[3] https://anastrophe.uchicago.edu/cgi-bin/perseus/citequery3.p...

If I let playing the lottery change how I interact with the world/prevent me from dealing with my situation, because I hope I will win, that 'hope' is a negative impact on my life.

If I encourage my friend who is down on their luck to buy lottery tickets so they can have hope, am I helping them, am I being kind?

> guess hope can be false now

"Hope is false if it is based on ignorance of the correct assessment of the probability that a desire is fulfilled or on ignorance with regard to the desirability of the object of desire. Hope is justified—realistic—when the hoping person knows and accepts experts’ judgement about the probability of hope fulfillment. However, I argued, what matters for evaluating a person’s hope is not only whether it is realistic, but also whether it is reasonable in light of the aim and goals for which the person strives in (the remainder of) his life

...a person’s hope that an (experimental) treatment may prolong his or her life or improve the quality of his or her life can only be called false when he or she thinks that the chances of personal benefits are greater than those estimated by experts. If he or she does accept their judgement, continuing to hope is realistic. Hope is moreover reasonable if it contributes to realizing what a person strives for in (the remainder of) his life" [1].

[1] https://pmc.ncbi.nlm.nih.gov/articles/PMC6900746/#s10