In $BrF_3$ molecule, the lone pairs occupy equatorial positions to minimize :-

In $BrF_3$, Br has 7 valence electrons; 3 form bonds with F and 4 remain as 2 lone pairs. So there are 5 electron pairs (3 bp + 2 lp), and the electron geometry is trigonal bipyramidal ($sp^3d$).
Repulsions decrease in the order: lp–lp $\gt$ lp–bp $\gt$ bp–bp.
In a trigonal bipyramid, an equatorial position has only two neighbours at $90^\circ$, whereas an axial position has three neighbours at $90^\circ$. So lone pairs placed in equatorial positions have fewer strong $90^\circ$ interactions.
With both lone pairs equatorial, they are $120^\circ$ apart (reducing lp–lp repulsion), and each has fewer $90^\circ$ contacts with bond pairs (reducing lp–bp repulsion).
This gives $BrF_3$ its T-shaped (slightly bent T) molecular shape.
So the lone pairs occupy equatorial positions to minimise both lone pair–lone pair and lone pair–bond pair repulsions.