You have always been able to read the RSS content for an article offline in LuckNews. LuckNews stores the article content in its database. However, it will only store the images for an article if you ask it to. If you always read articles while connected to the internet, there is no need to have LuckNews store the images. However if you want to be able to read articles offline, and also see their images, then you can do so.
To cache images, open the Subscription Information window for a subscription and turn on the "Cache images" option as shown below:
Note that if you select the 'Show full HTML' option for a subscription and try to read it while offline, the content may not appear the same as it does while you are connected to the network. Modern web pages contain references to many external resources, and not all of them are captured by LuckNews. If you both download HTML and cache images, some subscriptions look identical as you read offline as they appear while connected to the network. Other subscriptions do not look the same. Experiment with the subscriptions you use to find out which ones you can expect to be readable offline - I find most of them are readable, although they aren't all identical to how they appear online.
One last note regarding the ability to cache images. You may find that when you display full HTML pages for articles that LuckNews is slower to switch between articles - there is simply more data to fetch for articles when you are showing full HTML web pages. If this delay bothers you, try having LuckNews cache the images as well. This will speed up the transition to a new article as some of the data has been pre-fetched.