We should use 'to do', rather than 'doing', after 'it's adj.', right?
I don't see anything on the linked page that says that you can't use "doing" after "it's [adjective]".1 In fact, either construction (with an infinitive or a gerund) is possible. Both are examples of "extraposition" in which the subject is postponed and replaced by "it". Without extraposition, the sentences would be (for convenience, I've highlighted the extraposed subject):
First example sentence:
Finding our old photo albums and taking a trip down memory lane was lovely.
To find our old photo albums and take a trip down memory lane was lovely.
Second example sentence:
To be quite honest, doing nothing but re-visiting memory lane when I get together with my high school friends is growing quite dull.
To be quite honest, to do nothing but re-visit memory lane when I get together with my high school friends is growing quite dull.
It is common to extrapose subjects (as I did there!), especially when they are lengthy, as in those example sentences. ELL has an extraposition tag that contains some questions that you might find useful. (I've added that tag to this question, too.)
I also wonder which of 'adj. + doing' and 'adj. + to do' is preferred under what circumstances.
I won't address this issue, because another question on ELL already asks directly about it. If you're still confused, you may want to edit or otherwise bump that question so that it gets some attention.
1 That website seems to have problems. Within seconds I noticed a blatant error: "Restating a that-clauses as an infinitive clause". I'd be wary of whatever it says.