Effective fetching data algorithm
Whitespace formatting

Apply a linter that will give you PEP8 suggestions. Among other things, it will suggest the following:

import os,gc,queue


There should be spaces after those commas. It'll also suggest that there be one line per import.

class add_line:


should be

class AddLine:


and have a couple of newlines before it.

else :


shouldn't have a space before the colon.

f-strings

"https://ejje.weblio.jp/content/"+ w_list[1]


can be

f'https://ejje.weblio.jp/content/{w_list[1]}'


Falsiness

if len(fetched_text)== 0:


can be

if not fetched_text:


Don't repeat yourself

            li_ = list(map(lambda x:x.contents[0], fetched_text))
            li_.insert(0,w_list[0])
            self.put_queue(li_)


appears twice. Put it in a function or restructure your if blocks.

File iteration

with open(path) as f:
    while True:
        lines = f.readline()
        if not lines:
            break


First of all, your variable name is confusing. This isn't lines, it's line.

Also: just change your iteration to

with open(path) as f:
    for line in f:


As for this:

with open(path_w, mode='a') as f:
    # ...
    f.close()


Get rid of the close; the file is already closed at the end of the with.

main

You do check __name__, but you don't give all of that code function scope. You should move it into a main function. Otherwise, every one of those variables will be visible from other functions.