grrr, lost my previous attempted post Take #2.
You have the right general idea of how to hang your light string, just not quite the right details.
#1 - Brick and mortar are NOT structural, especially for a pull-out load situation. Once you get past a 'small' item attached to the brick (house number plaque, small flagpole bracket, that sort of thing), you really should anchor to the actual structure (the 2x lumber that is behind the brick 'siding').
#2 - Your lag-screw eye bolt looks like it is about 1/4" in shank diameter or so. Too small for the task, especially once the grape vines used your messenger cable as a trellis to grow on.
See here for a table of working loads for some FORGED closed-eye machine threaded (not lag screw threaded) eye bolts:
https://www.boltdepot.com/fastener-information/Eye-Bolts/Machinery-Eye-Bolt-Working-Load-Limits.aspx
When the load/force pulling on an eye bolt is no longer perfectly in-line with the screw shank, you really are supposed to use an eye bolt with a shoulder.
I know, this is not a 'critical' lifting situation (except to your wife, who is now upset about the broken and fallen light string). But IMNSHO, you really should just DoItRight and not do it Almost-Right.
And here, like most household projects, some level is overkill is usually a good thing. This thing doesn't have to fly or race, so make it at least a little bit 'stronger' than needed.
Use a bigger shank diameter closed-end eye bolt, anchored to the actual building structure (and not the brick/mortar 'siding').
Oh, and as mentioned, your electrical cable of the light set shouldn't have any 'kink' or pull on it. Support the cable with the messenger cable and don't have the electrical cable go through the carabineer.