Is there any way to get the neighboring towers’ info - MCC,MNC,LAC,CID?
No. A modem doesn’t need to know that unless it’s using the cell.
Neighbour LTE cells are identified by the combination of EARFCN and physical cell ID. These combinations need to be unique within the modem’s field of view.
You would need to build your own table by cross-referencing the EARFCN and PCI data with serving cell values as that becomes available.