Is there actually an episode of Lassie whereby someone deduces from Lassie's barking that Timmy is trapped in a well? [closed]

Apparently not.

From www.lassieweb.org:

Other television shows are always making jokes about Timmy being trapped in a well. Which episode was that?

Not to disappoint you—and all the writers who have milked this joke for years—but the answer is "none"! The classic Lassie joke has been for years this: "Bark! Bark-bark! Bark!" "What is it, Lassie?" "Bark! Bark-bark-bark! Bark-bark!" "What, Timmy's fallen in the well?" It's such a classic jibe that Jon Provost's autobiography was entitled Timmy's in the Well.

Then there's a really long list of things that happened to Timmy and a summary:

So of course the big joke is that never once has this kid ever fallen into a well! Paul almost fell into the well in "Her Master's Voice," and Uncle Petrie fell down a hole which was assumed to be an old well in "The Crow," but never Timmy. The only main character in the Lassie series, in fact, who actually ever fell down a well was Lassie herself, in Season 17's "Well of Love," a.k.a. "For the Love of Lassie."

No. In all of the show's 571 episodes, Timmy (or Lassie's previous owner Jeff) has never fallen into a well once. He was trapped in mines and pipes and many other things, but not a well; in fact, it was Lassie herself who was trapped in a well in a season 17 two-part episode. From Wiki:

"Timmy's in the well!" became a popular catchphrase years after the show's cancellation in reference to the many show situations in which Timmy's safety and welfare were placed in jeopardy. Although Timmy never fell into a well on the show, Jon Provost [who played Timmy] chose the phrase as the title for his 2007 memoirs, Timmy's in the Well: The Jon Provost Story. Provost points out that Timmy fell into abandoned mine shafts, off cliffs, into rivers, lakes and quicksand, but never fell into a well.

As for the origin of this misconception, it's hard to say. Kids fall into wells in real life, and people may have just assumed it happened in Lassie too. It's also possible that they confused mineshafts or pipes for wells, or misremembered the episode where Lassie fell down a well, and the mistake stuck.

Lassie pushed a water company man into a well on Jeffs collie. Lassie ran to get Gramps and mom, Ellen. In this episode Jeff wrote a note for Gramps to bring a rope.