It could be, dirt in carb, bad/ misadjusted/weak ignition module,
pinched
spark plug wire, bent flyweel key, bad plug.
But it's impossible to tell from a usenet post.

These things are almost all cheap for parts to fix, but labour could
cost
$100 or more.

It would help to know if the motor is a briggs & stratton, tecumeth, or
some
other make, but I'm going to assume Briggs.

Offhand I'd check the spark plug wire is not pinched/cut in the
starter-flywheel shroud where it goes out to the spark plug since that
was
removed shortly before the problems began. (to change the pullcord)
Even an experienced person can do this easily if they aren't careful as
there is only a slight bend in one spot for the wire to pass through
without
being damaged

If you can get the mower into the dark, try to start it and watch to see
if
little faint blue sparks may be going right through the wire to the
engine
case

Depending on the mower this wire can be part of the coil assembly, or
replaceable separately.
And sometimes just a bit of black electrical tape/shrinkwrap over the
wire
can get you going again.

A broken ignition wire is highly unlikely, but not impossible. I would
do a more
positive test of taking the plug out of the mower, but leaving it
connected to it's
lead wire. Then set the body of the plug next to a large metal surface
of the mower.
Pulling the starter cord should then produce a healthy spark at the
plug. If it doesn't,
she has an ignition problem such as a bad plug, ignition coil, etc.



But as already said, this is just an internet guess.

AMUN

The whole part of the gas was in passing, but not even an issue here.


Since the OP never did say what make the engine is, all of us are guessing

But as the original post said the lawnmower never had any problems.

Then the rope broke and was replaced.

Then it ran good for a while, then later acted up

On newer Briggs motors you have to pull the whole flyweel cover/shroud off
the get to the rope.
If you look at the spark plug wire it comes off the coil, and just sits in
one little bend between the flywheel shroud and the block.

When putting the cover back if the wire is in the wrong spot it gets
pinched.

And may not cut through right away but the mower vibration finishes it off.
A bit of moisture, and no spark

Then the spark may jump to the block rather than going to the plug.
if only the odd weak spark makes it to the plug, it will be hard to start,
but may still fire up if pulled fast enough

It's only a guess, but it would cause all the symptoms that were described


AMUN