Okay, you have your ID and SID, that's good.
Step 1.
Save in Lugia's room. Open up RNG reporter. Click "DPPt Time Finder." Go to the "DPPt Capture" tab.
Step 2.
Type in the your ID and SID in the required boxes. Click the "Shiny Only" checkbox. Under Method, scroll down to Method K. Put in the year you want to catch Lugia (2010). For Frames, put something acceptable, let's say 100. For Delay, put a minimum of about 700, a maximum of 999; we're going to use emloop to get a high delay. If you have a Synchronise Pokémon leading your party put in its Nature. Since you only want to find shininess, click Generate and leave the IVs, Nature and Ability boxes on blank/Any.
Let it geneate some results, then cancel the search, we don't need to look at all of them.
Step 3.
Pick one of the results it comes up with. Let's say, seed 01000376. This should be shiny with the given ID/SID. Right click it and select "Generate Times."
Step 4.
Pick one of the times that comes up. We'll go with the 28th of the 5th, 2010, at 00:58:59, delay 876.
Step 5.
Open up emloop:
http://pokem.client.jp/emloop.htm
You'll see a window like this:
In the red box, type your delay. In our example, that's 876. Click the button immediately under that, and a seconds value appears. Our seconds were 59; so do 59 minus the value that appeared, 14.6, to get 44.4, and put this in the green box.
Step 6.
Turn your DS on, and go to adjust the time and date. Set the date to 28/5/2010, and the time to 00:58. Press A to set the time at exactly the same time as pressing spacebar on the emloop programme. emloop will begin counting down. Turn your DS off and on again and quickly get into Pokémon Soul Silver. Hold down L, Start and Select. As soon as emloop reaches 0, press R to reset the game. emloop begins another countdown. Press A to skip the opening cutscenes, and then press A to Continue the game (at the continue/new game/connect to Pokéwalker screen) as soon as emloop reaches 0 for the second time.
Step 7.
This won't give the right delay as we need to calibrate for the time spend resetting. Catch Lugia and work out its IVs. Open up RNG Reporter. Click "DPPt Seed Finder" and go to the "Find Initial Seed by IVs" tab. Enter Lugia's IVs, and the time and date we're using (2010 5 28 00:58). You might need to adjust the minutes by one (2010 5 28 00: 59) to get a result. Check the delay of the resulting seed.
Step 8.
We need to adjust the delay in emloop. We're aiming for a delay of 876. The actual delay was whatever RNG Reporter shows. Subtract one from the other to get the difference. Our delay put into emloop needs to be this much bigger. Add this difference to 876 and put the new number into emloop, then repeat step 5 to 7 with the new, larger delay number.
Step 9.
emloop is now calibrated, and if we follow it exactly we should land on our seed. Note that we need an even delay. If you notice that you always get an odd delay, you need to correct for this by adding one to the year; so, use 2011 instead of 2010.
Step 10.
Now when we do the process we should end up in the game on the right seed. We need to check if the seed was right; we can do this with romstars translated programme, using the roamers method. Alternatively, since we're on a pretty low frame, we might not need to bother.
Step 11.
Now we work out the frame we want, and what we're on. With the seed I'm using in the example, we want to get frame 11. Depending on how many of the roamers are in your game our starting frame will vary. If two are out, I think we'll start on frame 3 to get Lugia (I might be mistaken here...). In that case, we'd need 8 advances, so we'd walk 256 steps with four Pokémon in our party, then catch Lugia. If the Lugia isn't shiny, work out its IVs and see what seed and frame it is on, then adjust accordingly; you might need to take a few steps outside the cave if you have the wrong number of party Pokémon instead...
To work out what frame our Lugia is, use step 7 to find the seed we're on, then copy this seed to the main window of RNG Reporter. Select Method K in the Method drop down, input your SID and ID where required, and click generate. Look on the list for Lugia's IVs.