Used different ports of microcontroller for LCD data pins
Looks like your software team has never heard of an Hardware Abstraction Layer (HAL) before.

You say 4 bit mode, so it's probably a character LCD. This is an incredibly slow LCD. It has no special hardware requirements. (eg: LCD controller or DMA)

A hardware abstraction layer should be fine.


  Issue with the design: My software team feels that if the data pins are on different ports, the code will be increased and latency between reading and writing increases


Maybe. Worst care you get one write for each pin. But in any other future design the addresses of the data pins is not a concern anymore.
Having the LCD pins sequentially on one port is utopic.