Line lock installation

If you have the line lock already, does it not have multiple ports on it?
Mine (and the one in your picture) have three outlet ports just for that reason.

One line for the front brakes in, plus three output ports.
(one for each of the front brake lines and one for a pressure switch for brakelights when the lock is engaged.)

Also be advized that the ports in the line lock body are not flared compression style, but plain pipe thread (so you will need the fittings to adapt them to flared style fittings, or they won't seal)

BTW, I have mine connected in the front brakes line right next to the master cyl and it has not been a problem of any kind, and made the install go really quick and simple.

Trying to find a pic so you can see how clean it came out.

Note that all I had to do was cut the line and feed it to the lock (one end of it in, and the other end to the out)
The lines are installed in the line lock with 3/16 steel compression unions, and one end of each union has the nut removed and is threaded directly into the lock body.

You will also note that there is no pressure switch or brake light wires visible.
That's because there isn't one. (but I do have brakelights when the lock is active)
I used the power supply side of the lock to send power to the brakelights with a wire section I designed specifically for that purpose.
It allows power to flow to the brakelights, but not from the braklights to the line lock.

Here's both images.