Found this story on Looney Tunes Wiki. An anon named "22.214.171.124" wrote it. It couldn't stay there since it was fanfiction, so I just copied-and-pasted it here.
One night, Sylvester and Taz were alone with Lola. Although Granny was starting to think highly of her, whenever they got a chance, the other Looney Tunes would talk about nothing but shoelaces. "Remember the time one had to be used to keep you away from trouble, Lola?" they would tease. Lola tried to sound louder by talking about Looney Tunes who got stuck in holes, and got stuck on mountains. "You talk a lot, small fry Lola!" said Taz. "A fine Tasmanian Devil like me has got something to say! I am the only Looney Tune who can pull the carriage express! When I'm not available, they need two Looney Tunes! Imagine that! I've pulled carriage expresses for many years, and I never once got lost! I appear to know the right path by instinct!" Every smart Looney Tune knows, of course, that the controller works the points to make Looney Tunes go on the right path, but Taz was so proud, he had forgotten. "Wake up, Lola!" shouted Taz the next morning. "It's almost time for the carriage express! What are you doing? Odd jobs? Oh, well, we all have to start small, now, don't we? Go on and get my carriages now! Don't be late!" Lola went to gather Taz's carriages. They were all shining with brand new paint. Lola was careful not to crash the carriages, and they followed her gently into the station, singing cheerfully, "We're leaving! We're leaving!" "I wish I was leaving with you." said Lola. "I would love to pull the carriage express, and go racing along the path!" Taz, with lots of growling, got ready to back up to the carriage express. Granny was in the carriage express, with other important people, and when they heard the guard's whistle, Taz started. "Watch me go! Watch me go!" cried Taz. And the carriages rolled along after him. "Grrr! Goodbye, small fry, Lola! See you tomorrow!" Lola watched the carriage express leave, and then, went back to work. She pushed some wagons into their places, and then, went to gather some carriages for another ride. Lola had just taken the carriages to the platform, when she heard a funny noise. It was Taz, trying to sneak into the station without being recognized. "Hey, Taz! Is it tomorrow?" asked Lola. Taz didn't say anything. He just growled. "Did you get lost, Taz?" asked Lola. "No. My path got lost. I was switched off the main path onto the loop. So I had to go around, and back again!" said Taz. "Maybe it was instinct!" said Lola. Meanwhile, all the passengers ran to the booking office. "We want our money back!" they all shouted. Granny climbed on top of a trolley, and blew the guard's whistle so loudly, that they stopped what they were doing to pay attention to her. Then, she promised them to find them another Looney Tune. "Taz can't pull the carriage express." said Granny. "Can you do it for us, Lola?" "Yes, Granny!" said Lola. "I'll do my best." So Lola was hitched up to the carriage express, and all of the passengers got in. "Work very hard, Lola!" cried Granny. "Let's go, let's go!" said Lola. "You're pulling us fine, you're pulling us fine!" sang the carriages. They crossed bridges and went past stations, everyone cheered, and they soon got to the station. Everyone thanked Lola, and Granny was most impressed. "Well done." Granny said to Lola. "How would you like to pull the carriage express sometimes?" "Oh, yes, please!" cried Lola. The next day, when Lola stopped by, Taz was pushing wagons. "I want quiet work for a change." said Taz. "I am teaching these wagons manners. You were good with the carriages, I heard. Good! We'll show them!" And he gave the wagons a hard push. Lola and Taz are now good friends. Lola sometimes pulls the carriage express so Taz can have a rest. Taz never talks about shoelaces, and they are both quite agreed on the subject of wagons.