There is a saying that "A bully is always a coward." Through his lie, Rajam Iyer is driving home this point: for all his bluster, the "newcomer" turned out to be a cheap coward who ran away in fear of Rajam Iyer.
‘Shall I keep a seat for you?’ asked Rajam Iyer.
‘No, my ticket is for Jalarpet,’ the newcomer answered and quickened his pace.
The "newcomer" is implying that he is only getting down at Jalarpet because his ticket was for that station, not because he was terrified of what Rajam Iyer might do to him in a brawl.
But, Rajam Iyer is not ready to let the "newcomer" off the hook that easily.
‘Did you hear that bully say that his ticket was for Jalarpet?’
‘Well,’ he lied, ‘he is in the fourth compartment from here. I saw him get into it just as the train started.’
Rajam Iyer is implying that the "newcomer" needed to be on the train, yet did not dare stay in the same compartment as him, which is why he jumped down in a hurry and boarded a compartment further away. Thus, he is establishing the "newcomer" to be a coward: the "newcomer" had no problem throwing his weight around on those weaker than him, but when push came to shove he showed his true colours and ran with his tail between his legs.
Why does Rajam Iyer say this? It's clear the bully left the train in fear of him, and quite likely that the bully was lying about his ticket being for Jalarpet, but why would Rajam Iyer just make up having seen him get back onto the train? What difference does this make to the situation or to anyone's perception of it?
It is clear to us as the reader that the bully left the compartment in fear of Rajam Iyer (regardless of his true destination), but I can imagine it not being so clear to a somewhat crowded compartment, and especially not to an apathetic crowd that looks at ongoing violence as entertainment:
Out of the corner of his eye he noted that the other passengers were waiting eagerly to see how the issue would be settled and were not in the least disposed to intervene.
Would such a crowd easily accept Rajam Iyer's psychological victory over the bully? Likely not, which is why Rajam Iyer wants to drive the point home with his little lie. The conclusion of the encounter has a lot more weight in favour of Rajam Iyer if it reads, "The newcomer got down in a hurry at Jalarpet because he was scared of sharing a compartment with Rajam Iyer," rather than "The bully got down in a hurry at Jalarpet because that was his stop to get down anyway."
Of course, not everyone buys it (perhaps some even saw the "newcomer" walk away on the platform), but at least he has the gratitude of the "meek passenger".
Though the meek passenger was too grateful to doubt this statement, one or two other passengers looked at Rajam Iyer sceptically.