As you asking for the names of the Government Lateral Entry Engineering Colleges of Coimbatore the names of the Government Engineering colleges are as follow :

Coimbatore

Coimbatore Institute of Technology, Coimbatore
Amrita Institute of Technology & Science, Coimbatore

the names of the other state City Government colleges that offered the engineering through Lateral Entry the names of the colleges are as follow :

Thapar Inst of Engineering & Technology,Patiala

JNTU, Hyderabad

Manipal Institute of Technology, Manipal

Maharashtra Institute of Technology, Pune

S.J. College of Engineering, Mysore

Sastra university

M S Ramaiah Institute of Technology

The Technological Inst. of Textile & Sciences, Bhiwani

D.J Sanghvi College of Engineering - Mumbai

Karunya Institute of Technology Coimbatore

Vishwakarma Institute of Technology Pune

KALINGA INSTITUTE OF INDUSTRIAL TECHNOLOGY bhubneswar

Mepco Schlenk Engineering College, Sivakasi

PUNJAB TECHNICAL UNIVERSITY