B757 pilot reported discovering a hydraulic fluid leak during landing gear extension on final approach. Flight crew conducted a go-around and landed safely.

Narrative

We arrived at the aircraft on time and proceeded with our preflight duties. We reviewed the logbook and took note the inbound crew had written: R-Trailing edge Flap Disagree EICAS and local warning when bringing up flaps after landing. During my exterior walk around inspect I also noticed the installation of new hydraulic lines and hoses on both right and left landing gear assemblies. Everything else appeared normal as usual. Start up; taxi; take off and cruise were uneventful. The ZZZ airport ATIS was reporting low IFR conditions with CAT Il and CATIll approaches into runway XX so we set up the aircraft for a CATIll approach into the ZZZ airport as the weather conditions required this. On the final segment we started the APU and configured the aircraft and extended flaps 20 and gear down. Shortly after gear extension we both noticed the gear door light illuminated and gear door disagree EICAS message. Given the condition of the aircraft we discontinued the approach and were given instructions to fly runway heading and climb to 3000 ft. We ran the appropriate QRH and checked the status page to verify HYD QTY. At this time we determined we had a major fluid leak indicated by .1 and the letters 'RF' in the left hydraulic system. A LHYD QTY and L HYD PRES EICAS followed. We [notified ATC] ; ran the appropriate checklists and determined an attempt to land in ZZZ with its low IFR conditions wouldn't be the safest course of action. We asked for the weather at the closest airports and ZZZ1 was reporting the best visibility and ceiling. At that time we requested a climb to 10000 ft. and vectors to ZZZ1.We shut down the APU and reviewed our plan of action. We continued with the checklist and it advised us of using alternate mode to extend flaps and gear. We both were aware of a gear door not being stowed so fuel burn was a concern. We decided to keep the aircraft at approximately 200 KIAS. We had 12000 pounds of fuel when we started the approach and about 9500 when we arrived into the ZZZ1 airport area. We set up for the ILS XY requested landing performance with the L HYD SYST failure. Our approach speed was set for 122KIAS / VAPP. We reported ready for the approach and were given vectors for a down wind. We began to configure using the QRH procedure. We extended the gear and final flaps 20 approximately on a 10 mile final and the checklist was completed. The landing was normal and we stopped straight ahead and set the parking brake; started the APU and shut down the engines with approximately 8000 pounds of fuel on board. We ran the shut down checklist. Ground personnel met us and visually inspected the aircraft. They advised us the aircraft was OK. They also informed us of a fluid leak coming out of the right landing gear well. I called ops on frequency and informed them of our situation and requested a tug to get us off the runway. This took some time and when they finally arrived they didn't bring a headset so there was no way to communicate with the ground crew. I called ops again and asked for the tug drivers cell phone. This proved to be the method by which we finally were able to communicate. We were finally towed off the runway on to a taxiway and remained there a short time while outbound aircraft from the ramp exited. We were towed into the stand and were chocked and stairs were placed. At this time the maintenance crew met us in the airplane and we gave a brief of the event that transpired. We ran the checklist and proceeded to write up the malfunction in the logbook. We also discussed the event briefly and finally called the dispatcher and gave him a brief of what had happened. After speaking with the maintenance crew we asked to see the area where the hydraulic fluid came from and he did so by pointing in the general area where the suspected leak was. It is evident this was a maintenance issue and not something we as an operating crew could have prevented. There are maintenance procedures and checklists while performingtasks performed much in the same way we operate the aircraft. The outcome of this event was a success from us the operating crew. We utilized CRM inside and outside of the aircraft to come up with the best possible solution that gave us the best outcome given our system malfunction and weather at our first intended airport of landing. With nothing more to state at this time I want to thank my First Officer for the exceptional support he provided.