Welcome to FT, and especially the Iberia Plus section.
Firstly some clarifications of terms:
Iberia Plus is the loyalty scheme of Iberia.
Iberia Plus uses Avios points as its (millage) currency for earning and spending.
Avios points are a common loyalty currency used by a few different loyalty schemes. (e.g. BA Executive Club - BA's frequent flyer scheme, IBplus - Iberias, Avios.com - a separate scheme, ...)
Each of these are separate schemes, someone can have accounts in each of them, each has their own balance of Avios points. Subject to some rules, Avios points (but not status points) can be moved between your own accounts in the different schemes.
The airline Avianca has it's own loyalty programme for it's customers, called LifeMiles (which replaced one called AviancaPlus). This scheme refers to its own millage currency as 'miles'.
Now, what loyalty point currency are you trying to spend. Lifemiles has nothing to do with Iberia Plus, or any of the Avios currency using programmes. Regardless of what you want to spend them on, the only person to talk to about Lifemiles miles is the Avianca Lifemiles programme. The currency only exists inside the universe of that programme.
Ok, so I will assume you have Avios points to spend. If you want to spend Avios points on Avianca flights this can only be done from Iberia Plus accounts - this is because Avianca are only a IB+ partner, they are not a British Airways Executive Club or Avios.com scheme partner etc.
Iberia, British Airways are in OneWorld alliance.
Avianca is in Star Alliance
But, as you have noticed, Avianca is an Iberia Plus partner:
http://www.iberia.com/web/webPartner...Partner=130093
That link has tables for how many Avios points you should need to redeem.
The footer of the redemption table also says it can only be done through the call centre.
So, to spend Avios points on Avianca flights, you need:
(1) To have an Iberia Plus account
(2) To move the Avios points into your IB+ account.
(3) To call Iberia Plus to do the redemption.
In terms of calling for the redemption, I'd try to work out yourself first if you think Avianca have reward seats on the date you want before calling.
Look in the Avianca section for how to check if they have seats available.
Also keep in mind they may make more seats available to their own members than they do to partners.
You could try using the ANA method etc to check for seats they are making avilable to *A members.
Personally, I'd only try calling IB+ if they are making seats available on to *alliance member airlines, if they are, they MIGHT be making them available to Iberia.
Hope that helps.
Hopefully someone else has actually redeemed from Iberia Plus on Avianca and can offer some advice.
(Other ideas: Fly LON to MAD on one booking, then do a separate booking MAD to Bogota with either IB or Avianca. That way you could avoid UK air passenger duty).