The sub_filter will munge text even when it shouldn't. Let's try some work-arounds:
Original: When you enable HTTPs for your site, SBI will turn links like "http://lugubrious.org" into "https://lugubrious.org".
Filtered: When you enable HTTPs for your site, SBI will turn links like "https://www.lugubrious.org" into "https://www.lugubrious.org".
Workaround: When you enable HTTPs for your site, SBI will turn links like "http://<I></I>lugubrious.org" into "https://<I></I>lugubrious.org".
Setting/removing formatting in BB2 can usually produce the effect of empty/no-op <FONT> tags to break up a string of text… or using zero-width spaces is probably more reliable.