likewise other cryptocurrencies network, if you transacting with litecoin or withdrawing any coin through litecoin the charges will be lesser of bitcoin charges,
That would be a temporary solution because altcoins like LTC are copies of bitcoin. So they inherit all bitcoin's shortcomings and they usually add more problems as well.
So if their usage grows, their fees would go up as well.
In fact one of the coins that were advertised as "will never have high fees" ended up having a much higher fee compared to bitcoin when it's network traffic grew back in 2017.
why can't bitcoin maintain same transaction fees with one of altcoins.
Two reasons:
1) These altcoins are not used nearly as much as bitcoin is. So their blocks are mostly empty and there is no competition for the block space to push the fee rate up. If their usage grows, their fees shoot up as well.
2) Their prices are far lower than bitcoin. For example if you pay a high fee of 0.0001 for a bitcoin tx, that is about $6 but the same fee of 0.0001 in litecoin, that is worth $0.007 because of how much lower LTC price is compared to bitcoin. This is why the fees you pay in altcoins usually don't
seem high even if the fee-rate were actually high.