grammar - Does anyone know which おり this is?

彼女は表情が生き生きとしておりとてもかわいい。

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?

Answer

Let me have a go at this:

• 
  

  彼女{かのじょ}は: She/Her (establishing context)

  
  


• 
  

  表情{ひょうじょう}が: expression (with nominative case marker)

  
  


• 
  
  

  生{い}き生{い}き: vividly, lively

  
  


• 
  

  して: Verb conjunctive form of する

  
  


• 
  

  おり： 連用形 of　居る{おる} (To be/exist for animate things) This should be the verb you're looking for

  
  


• 
  

  とても: intensifier

  
  
  


• 
  

  かわいい：　pretty

  
  

1. 
   

   The verb is 生き生きとして居る, the subject is 表情. Combining them yields "There is a vivid/lively expression"

   
   



2. 
   

   Context is 彼女

   
   

   Combining 1. and 2. yields "For her, there is a vivid lively expression"

   
   

Now put the verb in 連用形 to get:

3.彼女は表情が生き生きとしており

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.彼女は表情が生き生きとしており

The other sentence is とてもかわいい ((She) is very pretty)

Combining them yields "She has a lively expression, she is very pretty"

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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.

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*Extracted from nihongoresources:

One of the uses of the 連用形 is to join up several sentences as subphrases into a large continuous (which is what 連用 means) sentence, similar to how in English for instance you would join up two sentences by putting a comma between them and if necessary changing the phrasing on the first sentence just a tiny bit. If we look at an example you might get an idea of how this works:

日本語：　花が咲く。 English: Flowers bloom.

日本語：　鳥が鳴く English:　Birds are chirping..

日本語：　春が来た。 English:　Spring has come.

We can combine these into a single sentence:

日本語：　花が咲き鳥が鳴き春が来た。 English:　Flowers bloom, birds are chirping; spring has come.