The main organelle involved in modification and routing of newly synthesized proteins to their destinations is:

Endoplasmic reticulum, along with the Golgi apparatus, is involved in the transport of proteins and enzymes to their destination, i.e., within the cell and also outside the cell. Hence this is the right answer. While the lysosome is also involved in the transport of the hydrolytic enzymes, but it is not the major transport mechanism in the cell.