Horns:
Lew Soloff plays exclusively on Bb Trumpets made by Blessing, a division of Verne Q. Powell Flutes

Other Instruments:
French Besson vintage Flugle
Schilke P5-4 Piccolo Trumpet (Gold plated)

Mouthpieces:
Bach Mt. Vernon 1/4C
For most improv and also recording work that doesn't go into the extreme high register. I also use this mouthpiece for playing C trumpet

Monette Custom
(a copy of a Schilke mouthpiece that I lost)

Lavscy Custom
(also a copy of a Schilke mouthpiece that I lost)
For lead work and soloing when I want to play high and long like over a big band or a loud electric gig. I sometimes use it because I prefer the brighter sound for the style of the music played. The lost Schilke was called Soloff 1. The closest stock mouthpiece to it that I know of is probably a Schilke 14A4A.

Marcinkiewicz
E12.4 with a 30 throat
For extreme high register and i also like the sound for soloing somtimes.

Bach 7 E Coronet
117 backbore for the Schilke P5-4 Piccolo Trumpet

For Fluglehorn
I use a very deep mouthpiece with a 14 throat. For section work I sometimes use a more stock mouthpiece like a 3C Flugle.

Mutes:
Ray Robinson cup mute
Stone Line red cup mute
Joral copper Harmon mute
Alessi mute
Joral mute
Wooden straight mute
Toilet plunger