If I understands your question correctly, I think this will solve it:

with jsonlines.open('yourTextFile', mode='a') as writer:
    writer.write(...)

As you mentioned you are overwriting the file, I think this is because you use mode='w' (w = writing) instead of using mode='a' (a = appending)

import jsonlines

with jsonlines.open('example.jsonl', 'r') as jsonl_f:
     lst = [obj for obj in jsonl_f]

The jsonl_f is the reader and can be used directly. It contains the lines in the json file.

You have a JSON Lines format text file. You need to parse your file line by line:

import json

data = []
with open('file') as f:
    for line in f:
        data.append(json.loads(line))

Each line contains valid JSON, but as a whole, it is not a valid JSON value as there is no top-level list or object definition.

Note that because the file contains JSON per line, you are saved the headaches of trying to parse it all in one go or to figure out a streaming JSON parser. You can now opt to process each line separately before moving on to the next, saving memory in the process. You probably don't want to append each result to one list and then process everything if your file is really big.

If you have a file containing individual JSON objects with delimiters in-between, use How do I use the 'json' module to read in one JSON object at a time? to parse out individual objects using a buffered method.