This is not a philosophical discussion, there are equations for a reason and the whole debate needs to be in a spreadsheet.
That said, both of these items are for use against armored targets, ie tanks & bruisers. Unless a carry has decided to build tanky they usually die in a split second if they are caught in the open anyways. 1-2 AA + a nuke from your AP = gg enemy carry.
I was bored and ran this all through a spreadsheet based on kog'maw's auto attacks at lvl 18 with standard build items, (2x doran, boots, IE, PD) and compared adding a BC vs LW.
Generally, on a target with <155 armor BC is better than LW over a 5 second engagement.
I chose 5 seconds because in 5 seconds is enough time to do ~2,000 AA damage to a target taking into account armor & crit chance.
I used kog'maw as my AD example because he is my AD of choice did not add in W active damage which benefits heavily from BC giving extra hits in longer fights due to + asp.
Assumed +30% asp from Q being lvl 5 at lvl 18.
Used Kog's base ASP & + asp per level (varies by champion)
As my example target I used a Wukong with +flat armor yellows, Atmongs, Wiggles, Triforce.
This example Wukong had 164 armor at lvl 18 and over 5 seconds LW did more damage.
Messing around with fight duration, at 10 seconds the break even is 165 armor vs 155 armor at 5 seconds
Duration of 3 seconds the break even is 82 armor since the initial hits on a BC do considerably less due to needing multiple hits to get full stack.
Interesting things to consider:
In this specific use case:
3 second fight = 5 attacks for each combo
5 second fight = 8 LW and 9 BC attacks
10 second fight = 17 LW attacks and 19 BC attacks
I feel like a 5 second fight sounded right on the surface but when cosnidering the number of attacks the 3 sec encounter seems much more "actual". landing 8-9 hits on a target seems excessive unless it is a tank and I am the only person hitting them. I feel like most carries die in 2-3 hits and bruisers usually get hit byt the first barrage of AP dmg.