לזכות משה יהודה בן פעשא דינה
The Halacha is that when one is busy tending to a lost object he is פטור from giving tzdaka. The question is whether one is allowed to get involved with a lost object with the knowledge in advance that while he is busy with it a poor person will come and ask for tzdaka.
A Proof That You Should Do The Mitzva
The Ritva [Succah 25a] asked why we need a pasuk to teach the rule of עוסק במצוה פטור מן המצוה when it is logical to assume that when one can't fulfill both mitzvos he should not stop what he is doing and involve himself in a different mitzvah and it should even be forbidden [as a lack of respect for the present mitzvah]? His second answer is that the pasuk is teaching that even if he has a set mitzvah at a set time, מצוה קבועה בזמן קבוע, to do [like Krias Shma], and another mitzvah comes around beforehand that would necessitate nullifying that mitzvah, he should still do it despite the knowledge that he is thereby missing out on his מצוה קבועה.
According to this answer, even if one knows that a poor man is coming along later he may still take care of the lost object.
A Proof That One Shouldn't Do The Mitzva
On the other hand, the Shulchan Aruch [72-2] says that one shouldn't get involved with the mitzvah of burying a dead person if it is almost זמן קריאת שמע if he knows that he will miss out on קריאת שמע if he takes care of the מת. So we see that one SHOULDN'T start a mitzvah knowing for a fact that he will miss out on a later mitzva. In our question this would mean not to deal with the lost object until AFTER he gives the tzdaka.
[מאוצרות הגר"א גנחובסקי זצ"ל]