B737 First Officer reported operating an aircraft with a long history of leading edge flap asymmetry discrepancies. This aircraft had a repeat discrepancy occur during approach to landing. The flight crew performed a go around and complied with the QRH procedures and rejoined the approach and landing at destination airport.

Narrative

The aircraft had a history of flap issues and issues with the EECs that the Captain and I discussed in ops before the flight. In the carry forward items section of the release there was a long time fault with the #1 EEC. Then in the log history on Day 0 the aircraft had a leading edge flaps transit light stays on write up. There were a series of write ups with the flaps in the history saying #2 transit light on. The first one starting on Day 0; then Day 1 was the second occurrence; then Day 2; then on our flight on Day 3. All of these write ups had the leading edge flaps transit light on. We did discuss this history together before the flight.Normal flight up until top of descent point. Thunderstorms were starting to pop up into central [state] and there was holding into one of the airports; we think it was ZZZ1. Frequency was very saturated and difficult to get any word with ZZZ2 center or Center. We asked for lower 4 times on frequency before given our first descent and that this point we were 5000+ feet high on the arrival. When finally given descent via ZZZZZ1 landing east we told ATC we would be do are best but were already very high. Speeds on the arrival were complied with and full speed brakes were used from the TOD which was my best guess FL350 down to a cleared to bottom of 6;000 feet. When we switched to approach we were vectored off the arrival for traffic and told to maintain 6;000 feet. Approach gave us a vector off the arrival and then vectored us on ILS approach course. Thunder storms were building all around ZZZ and there were some buildups and rain that we went through when being vectored and re-vectored onto the arrival. At some point during these vectors back onto the ILS Runway XXL approach course we were given a speed reduction to 210 knots. This occurred somewhere on the base leg to final. At that time the Captain called for flaps 1. All indications with the Flap position indicator showed flaps 1; the handle was at flaps 1; but the LE Flaps transit light was still illuminated. A quick glance up at the Leading Edge Devices annunciator panel showed 1 amber light; the rest were green. The amber light was located on the left hand side underneath the flaps 1 number at the top of the annunciator. We were concerned with the approaching thunderstorms to the ZZZ airport so I pulled out the paper Quick Reference Handbook and we began running through the procedure while continuing on the approach. Went to the flight controls tab; then the leading edge flaps transit light page read the notes out loud quickly and then read through point 1 where it gives you the option to choose 1. We read through the first one and ruled it out and had a quick discussion that were was no roll or any indication of any asymmetry. Read the second one and again after some quick discussion agreed it was our problem. Went to step 7 and started to plan for a flaps 15 landing. We set Vref 15 +15 knots. This is where I made an initial error. I selected flaps 15 Vref speed and then put +15 in the wind additive so I think the flaps 15 speed was 160 and I put the plus 15 in the wind additive for a speed of 165 knots initially. Then step 9 is use normal wind additive winds were like 150@9 at the time so would of been + 5 but I did not change anything at this point. Step 10 is to put the ground proximity flap inhibit switch to inhibit so I confirmed that with the Captain and did that. Somewhere right in here we got are last turn on to the approach course and were cleared for the approach. The next step was to calculate landing distance so I had to go to my IPAD this the tables are removed in the Quick Reference Handbook for that. Hit they hyperlinks for the 900ER and found the table and read out the landing distance first for the Trailing Edge Flap Asymmetry Flap lever 15 and then I realized this was not the right table and found the Leading edge flaps transit flaps 15 aircraft condition. We were approximately 145;000 pounds so I read out 5;000 feet needed for good braking and 7;000 for medium. I then looked at the adjustments to landing distance and the only one that applied was the add per C above ISA and it was minimal. Then went to step 3 for the 15% safety margin and if it went down to medium braking we needing about 8;200 feet of runway and less than 6;000 feet for good. The rain was not hitting the airport currently so we expected to have 600 braking. The runway is listed as 9;000 feet long on the 10-9 and 8;400 ft. available beyond the threshold. I did all this as fast as I could and while we were intercepting the glide slope and starting down on the approach. All through this the center and approach frequencies were completely saturated with constant communication from ATC to other aircraft and us with no real significant breaks between radio transmissions. I read aloud steps 13 and 14 and then went right into the deferred items because we were at that point already. Captain called for gear and flaps 15 somewhere in the middle of the deferred items checklist we finished the checklist somewhere between 1;500 feet and 1;000 feet. Captain asked if we were good and we both agreed we were to continue the approach. I double checked the whole procedure reading it quickly through again and realized I set the flaps 15 speed wrong so by the I think Vref 15 was 149 I added the 15 knots to 164 and put that in on the speed line and then changed the wind additive to +5 so we had an approach speed of 169. I did this right before we were at 1;000 feet. At some point during all of that we were switched over to Tower and cleared to land. There was a corporate jet on the runway and he was being told told we were fast approaching and to vacate the runway. Then given expedite instructions and then a little above 500 feet. tower issued go around instructions to us.We were given a heading slightly off from runway heading an initial climb to 2;000 feet Captain gave all the correct go around commands we went to heading select and flew the Tower assigned heading; we had a discussion of the missed approach instructions because Captain wanted to make sure he heard them correctly and also a discussion about going all the way to clean maneuvering speed or leaving flaps down. Captain wanted to try and recycle the flaps to see if we got the light again. So we did go all the way to flaps up and after takeoff. Eventually Tower gave us a turn to the downwind and a climb to 4;000 feet and switched us back over to approach. Approach re-vectored us on to the course for another ILS XXL approach. Captain redid an abbreviated approach brief and then we selected flaps 1 again and go the LE Flaps transit light. We went through the Quick Reference Handbook again and completed all the steps to the deferred item landing checklist. We completed the deferred item checklist after the gear was selected down and that finished the procedure. While being vectored I did let approach know that we were going to have a final approach speed of 170 knots we never [requested priority handling] or let any outside source know of the flap system malfunction. Our main concern was getting into the field before the thunderstorms passed over it. Captain made an uneventful flaps 15 landing. We exited at [taxiway] 1 and were told to go straight to ramp and ramp told us to go into [the gate]. We complied with instructions and safely parked. Completed the parking checklist and then called ops to let them know of the maintenance problem and Captain put the write up into the ELB.