was translated awkwardly on ALC as
She is very pretty for the liveliness of her expression.
Which おり is this? I think I know it from the polite しております but is it here wielding more expressive meaning?
Let me have a go at this:
Now put the verb in 連用形 to get:
One of the uses of the 連用形 is to join up several sentences as subphrases into a large continuous sentence.*
One sentence has been established, which is in 3.
The other sentence is
Combining them yields "She has a lively expression, she is very pretty"
EDIT: Regarding your comment on trying to introduce a "because" nuance.
You can use the て-form of the verb to introduce an implicit sequence of events. (Weak causal relation)(If you want a stronger causal relation, use から)
See Verb Grammar - The Verb Conjunctive Form(You have to scroll down a little bit)
The difference between linking sentences with て-form and linking with 連用形 is that there is no implicit sequence of events when linking with 連用形.
*Extracted from nihongoresources:
It replaces the verb stem
The construction in your example uses a verb stem to continue another predicate after it as in:
When you use the verb
Those people replace
When it is followed by an affix, the shortness of the stem is compensated by the affix, and it does not sound bad, so both forms are allowed:
The translation that you got is a good one for a literal translation.