@MarioUrroz 

Hey

The LAN port on the second AP is only really designed to allow the APs to be tailed (chained) together directly.    Basically you could run another AP (AP3 for example) via a LAN connection to the port in AP2, hopefully that makes sense?  :)

In answer to your query, its basically that you need LAN capability in building 2?     If you really dont want to run cables, then I personally would look ay buying an AP that can do "client mode" and use it to connect to the WLAN.  

Incase you are not familiar, client mode is when the AP is switched over from an AP to a client.  Namely it will connect to your WiFi (the eap225) as a WiFi client, then anything you plug into the APs LAN port will get LAN connection.  If you need more LAN ports, plug a hub in here also or look for a AP that has 4 lan ports (not so common now)

In short it will be like this

ROUTER  >   AP1  over mesh to   AP2  >    CLIENT AP connected to AP2 via WiFi  >   LAN port on CLIENT AP  >   whatevever device you want cabled in...

Below is an older article, but the process is correct.. 

https://www.tp-link.com/ae/support/faq/1606/

  @MarioUrroz It sounds like your goal is to pipe the network into building #2 and also maintain wireless performance outside the building.  I don't think Mesh is the way to do that personally.  Ditch the Mesh. Get a POE Switch and a CPE. Mount CPE outside building #2 aimed at EAP #1.  Connect EAP #2 and CPE to the POE switch inside building #2. This will provide power to those devices and pipe the network inside. You can add a wireless router inside as well.  You will have a very strong connection between EAP #1 and the CPE on building #2,  strong wifi outside building #3 from EAP #2, and strong wifi and wired connections inside building #2 via the wireless router.  I have virtually the same setup. I tried Mesh and while it worked, my main goal was maintaining as much throughput as possible.The Mesh failed at that but the above configuration gave me virtually full specified ISP bandwidth for my wireless and wired connections.  You will still be able to configure both EAPs with your controller, they will just show up as wired and will not be Meshed. There is no need for a Mesh here and actually no need for a controller. You can access each AP via web interface using IP address.

Below are two screenshots from my phone. #1 is outside standing next to an EAP225 Outdoor Meshed to the Central EAP610 Outdoor.

#2 is inside my RV, connected to my wireless router that has a wired CPE connected in client mode to the same Central EAP610 Outdoor. Of course my PCs wired to the router also get the full bandwidth.

  @RickJamesBish 

The origional poster had indicated that the wireless network was working great, if that is the case and the range is short enough for Mesh between the APs then I would recommend against adding a CPE.

CPE is really designed for long distances and can actually degrade performance at short range (less than 50m) due to its massive transmit power, if mesh is working to a satisfactory level then my advice is to stick with what he has. 

  @Philbert I have been running 3 CPE710 under 50 meters without any degredation for over a year,  and as mentioned it provides full bandwidth that Mesh at even shorter distance could not provide. You can also reduce power of the CPE if there were an issue but I have never found the need. If he does not mind sacrificing some of the bandwidth then he could certainly go the route of putting an AP inside and connecting in client mode to EAP2, but then you are losing even more by going wireless through the building. It will not be able to match the performance using the CPE as diagrammed but then he may not be worried utilizing all the bandwidth available.