IE should be a lot better than LW, since it's 3800g vs. 2300g.
The fair comparison would probably be LW+BFSword vs. IE, or LW+Brutalizer vs. IE, since then you're spending about the same amount of money. Or maybe LW vs. BFSword+Pickaxe or BFSword+Cloak.
Let's assume you have 50AD and a 1.0AS to start.
With an IE, you have:
130AD, 25% crit, crits do +150% damage. So every 4 attacks you'd do (130 + 130 + 130 + 130 * 2.5) = 715 damage, then mitigated by armor. Of course the damage is unpredictable, and this is the average result.
With an LW+BFSword you have:
140AD, so in 4 attacks you do: 140 + 140 + 140 + 140 = 560 damage, then mitigated by 35% less armor.
With an LW+Brutalizer you have:
115AD, so in 4 attacks you do: 115 + 115 + 115 + 115 = 460 damage, with 35% less armor and then -10 armor on top of that. (You also have 10% CDR that I'm not taking into account in any way here.)
Let's look at how these options do as your opponent's armor varies.
With 50 armor (33% reduction):
IE does 715 damage, reduced by 33% to 480.
LW+BFSword does 560 damage, but reduces effective armor to 32.5 (~25% reduction), so you do about 420 damage.
LW+Brutalizer does 460 damage, but reduces effective armor to 22.5 (~20% reduction), so you do about 370 damage.
With 100 armor (50% reduction):
IE do es 715 damage, reduced by 50% to about 360.
LW+BFSword does 560 damage, but reduces armor to 65 (~40% reduction), so you do about 336 damage.
LF+Brutalizer does 460 damage, but reduces effective armor to 55 (~35% reduction), so you do about 299 damage.
With 200 armor (67% reduction):
IE does 715 damage, reduced by 67% to about 235.
LW+BFSword does 560 damage, but reduces effective armor to 130 (~57% reduction), so you do about 240 damage.
LW+Brutalizer does 460 damage, but reduces effective armor to 120 (~55% reduction), so you do about 207 damage.
With 300 armor (75% reduction):
IE does 715 damage, reduced by 75% to about 180.
LW+BFSword does 560 damage, but reduces effective armor to 195 (~66% reduction), so you do about 190 damage.
LW+Brutalizer does 460 damage, but reduces effective armor to 185 (~65% reduction), so you do about 161 damage.
TLDR:
Early on, LW+BFSword breaks even with IE at about 200 armor on the target given those base stats.
However, with the LW you're not reliant on RNG. If you don't crit in a sequence of attacks, you're doing less damage with IE. Also LW/Brutalizer benefit physical damage skills and crit usually doesn't.