What you should do with timid is search for anything zero and up on Attack stat, because you may have a good timid spread with a really low attack stat. Why don't you give me your SID and OT and I'll check.
PID: bdf33f23 (TIMID, ability 1) 31/25/25/31/24/28 (Seed: fe0b0b81 Method 1: 575, J (synch): 448, J (no synch): 564, K (synch): 452, K (no synch): 546) HP BUG 40
This has a 2935 delay, but don't let that scare you. It is an awful lot of phone calls. It may be simpler to kill off those roamers, because all the other seeds for this spread had really high frames.
But if you give me your OT and SID, I can check to see if you do happen to have a better shiny timid spread.
Btw, you need to do your frame advancements outside the cave. Then you walk in and catch Lugia. If you have enough extra frames, you test the frame advancements of walking into the cave by going in and out once and then making sure of where you are with Elm calls. If there was no advancment, then you advance by Elm as usual to one before your target and go get Lugia. If you do have a frame advancement from walking in and out, then you must account for this when you do your frames so that you will be one before the target frame when you walk in.
You may be able to get the same spread with a higher frame. What's the seed you're currently using? I'll check on PokeRNG to see if you can still do this with a higher frame.