Where do I connect my new T-Stat in my Weil Mclain boiler
Your boiler wiring is a bit tricky...
Your boiler, along with some other Weil-McLain boilers, is a rather tricky beast in that it does not supply 24VAC to the thermostat connections at all times.  Instead, it only supplies 24VAC to the 'stat if the low-water cutoff has not opened its contacts to shut the boiler off, which is a problem for a smart thermostat because without that constant supply, it might &quot;lose its mind&quot; if the low-water cutoff on your boiler ever kicks in.
...however, we can overcome this, but we'll need to pull a fatter cable to do so
The good news, though, is that like many modern thermostats, your Lyric T5 supports what are called two transformer systems, with separate power sources for heating and for cooling.  Furthermore, in these two transformer systems, the Lyric T5 pulls power from the cooling transformer (Rc/C).  This is good because it means that once you pull a fatter thermostat cable through to have enough spare wires, it's possible to wire your thermostat so it gets constant power, yet doesn't inadvertently bypass the low-water cutoff.  (Consider that bypassing the cutoff would a) void any insurance you have on your house and b) render the boiler vulnerable to blowing up due to trying to run with insufficient water.)
You'll want to pull a fat cable for this, by the way; I'd recommend an 18/7 or 18/8 cable at a minimum so that you leave spare wires for the next installer to use.  Once you have the new cable in:

Red goes to R on the boiler and Rc on the thermostat base
Brown goes to G on the boiler and Rh on the thermostat base
White goes to Y on the boiler and W/W1 on the thermostat base
and Blue goes to C on the boiler and C on the thermostat base

This way, the thermostat gets constant power from Rc and C while connecting Rh to W/W1 to call for heat.  Once everything's in place and wired, I would run a simple test after turning things back on, though:

Crank the heat up to maximum to cause a call for heating
Head down to the boiler and activate the TEST function on the low-water cutoff, or simply unplug it from the boiler if your LWCO lacks a TEST function
Make sure that the boiler shuts off (stops heating) while the thermostat stays on when the LWCO is in TEST mode (or unplugged)
Once the test is concluded, make sure you reset the LWCO to the operating mode (or plug it back in if you had to unplug it) and set the thermostat to your desired temperature