A brother 15 years old is home with two sisters 16 and 17 years old, can he call over his friend to sleep with him for the night,
This is not permitted. [Even if it would be permitted, it would not be recommended.]
According to the Rema, two men and one woman are sufficient for yichud during the day.
For two men and two women, some write that it is permitted even according to the Beis Yosef — see Bach, Even Ha-Ezer 22; Chelkas Mechokek 22:6; Taz 22:3, Chikrei Lev 19; Otzar Ha-Poskim 22:27:2. Others dispute this (see Aruch Ha-Shulchan 22:9, Pischei Teshuvah 22:5; Igros Moshe Even Ha-Ezer Vol. 4:65:15).
However, this apparently helps specifically for yichud during the day (like the case of two men with one woman, which helps specifically for the day alone), and not for yichud at night.
The other issue is the matter of the brother acting as a shomer. Although a brother can be an effective shomer, this is true for the day, and not for the night, where two shomrim are required (with some exceptions).
Therefore, one cannot be lenient for this.