This work reports a novel mid-infrared (MIR) lateral Ge1-xSnx (x = 6%) waveguide-based phototransistors (PTs) on a silicon platform. A lateral device structure is proposed to enhance the optical confinement factor (OCF) and the optical power through the i-GeSn waveguide, thereby, increasing the optical responsivity of the PTs. The proposed devices are investigated using multiphysics simulation. The designed PTs are investigated in terms of the Gummel and output characteristics under both dark and illumination, 3dB bandwidth, optical gain, and responsivity. The effect of lateral scaling on various figure-of-merits of PTs is also studied and in return, helps optimize the device structure to get the highest optical gain, responsivity, and 3-dB bandwidth at 2000 nm. The theoretically optimized PT achieves the maximum optical gain of 1650 and responsivity of about 308A/W at 2000 nm, with V_BE=0.3V and V_CE=1 V. In addition, the device exhibits a record-high 3-dB bandwidth of >55GHz. Thus, the encouraging electrical and optical performance of the proposed PT manifests it as a great potential candidate for the 2000 nm band.