Allison and Lillia is a children's show. At least, I assume it's a children's show, as few adults would stand for such massive plot holes, idiotic character motives, and unbelievable action sequences. Not that children's shows should be allowed to have such low standards, but adults often assume children are too stupid to notice the difference.
The story is broken up into several arcs of about 4 or 5 episodes each. The arcs usually occur some several months apart, although midway through there is a gap of about 16 years, and the main characters switch from Allison and Will to Lillia and Treize. The stories of each arc may reference and have roots in previous events, but mostly they stand alone, so this series is somewhat like a collection of short stories centered around a common group of characters.
The stories range from adventures searching for a lost treasure that can stop a war between two nations, to uncovering and foiling various dastardly schemes by a parade of generic villains who often have baffling motives. The sense of danger present in the adventures decreases as it becomes increasingly obvious that no one is really willing to kill any of the important characters despite plentiful and convenient opportunities to do so. There is also always some faint romantic intrigue, usually one main character yearning for their painfully oblivious partner. While the awkward moments do make for some amusing scenes, the frustration negates many of the benefits of their inclusion.
The characters in the series are surprisingly flat, and many times incredibly carefree. Royalty and secret government agents too often rely on their emotions and whims. Fortunately for them, and the world at large, so do the corrupt politicians and businessmen. The main characters fair little better. Allison, the show's first protagonist, is a decently strong, if flighty, independent female, and a military pilot, but she is constantly pining for her childhood friend Will, who is comically obtuse to her feelings. It is primarily their interaction that carry the first half of the show, until Will changes drastically in the third arc due to a ridiculous plot twist.
The second half of the series switches focus to Allison's daughter Lillia and her friend Treize, who has a secret that EVERYONE else knows. Treize is also keen to a secret about Lillia that, again, she is the only one oblivious too (with a later character even reaching the conclusion within moments of meeting her). Personality wise, Lillia and Treize are very much echoes of Allison and Will, with the girl being the energetic and free-spirited one, and the boy being practical and subdued, but this time it is the boy with the one-sided crush. Unfortunately for Lillia and Treize, they lack the chemistry of their predecessors, and the pre-existing characters generally outshine them.
If you care at all about a sensible plot, though, this will all be overshadowed by a complete disregard for logic and Occam's razor. The surprises the show springs (the one's it doesn't constantly hint at, anyway) are completely unpredictable because no one in their right mind would make such decisions. In the last arc, multiple elaborate stages are used to kidnap the least likely person to ransom them for another who could have been taken several times early with less effort.
The artwork often captures the essence of the surroundings, and locales give a sense that they are genuine. Character designs are fine, and aircraft deserve special mention, considering how important they tend to be. Trains, however, tend to be unrealistically roomy (although that's a minor issue). Action scenes are passable, but do little to convey the excitement one would hope for.
The opening and closing numbers are mellifluous pieces, soft and soothing, which often puts them at odds with the events occurring in the story, but they remain enjoyable. The background music for the series on the other hand, is often overbearing, often beating the listener over the head with the sense that a given scene is supposed to be tense, suspenseful, or dire.
There are better shows out there. Try Kino's Journey if you want the sense of adventure, or maybe Last Exile for young people caught up in trying to end a war. Allison and Lillia, give it a miss.