If you have a cut on your lip, can you catch hiv or syphilis if u share a cigarette with someone?

Possible but: Unlikely. You could get the infection if the person you are sharing cigarette with is infected, has enough agent in the saliva or has cuts on his/her lips and the cigarette is contaminated. There would have to be sufficient inoculum to get into the cuts on your lips. I can say for sure that smoking is bad for you and you should quit while you are ahead.