Irises you should plant now. It's important to choose a sunny location and do not bury the rhizome. Just sit it on the surface, burying only the roots. The rhizome should be exposed to sun & air for flowering. It will sprout leaves and enlarge before winter sets in. Let it die back naturally with the onset of winter, it will fall into its natural growth cycle.

Alliums & Lilies are related and should be planted early spring.

Sorry, but many Alliums are cold temperature growers and should be planted now. Which Alliums are you asking about?
Bulbous iris should also be planted now. Again which ones are you planning?
Lilies may be planted as and when you buy them.
Now sure that you can determine the flowering time of Alliums by varying the planting time though.

Agree with Owdboggy- I doubt you'll be able to delay the alliums flowering, and assuming they're hardy varieties, they need planting right now, preferably within the next week at the latest, while there's still a little warmth in the soil, along with Iris reticula bulbs (unless you mean tall bearded iris, which are rhizomes, should be planted now, but not entirely buried). If you mean Lilium varieties when you say lily, if they're hardy, they can be planted now

Allium bulbs should be planted the sooner the better, but they are pretty hard wired to bloom in late spring/early summer, around May or early June in the UK, I would expect. It is a bit late to plant Bearded Iris: the plants probably won't be harmed, but they may not bloom next year. If you want to give it a try, I would select mid-season to late bloomers, or some of the summer repeat bloomers, such as 'Summer Olympics', for your best chance of blooms in July. With Lilies, the taller Trumpet or Oriental hybrids should bloom in that time frame. As Owdboggy says, plant them as they become available.

And just out of pedantry, Alliums and Lilies are not actually related, sorry Bathgate.

Yep, both Monocots, but different orders within that. That said, even being in the same family wouldn't be an indication of when to plant: Daffodils (Narcissus) are planted in the fall, while their cousins the Rain Lilies (Zephyranthes) are best planted in the spring.
You might get away with planting Alliums in the early spring, but they will do much better planted a few weeks before hard frost, so they can grow more roots.

Not so Owdboggy. Alliums (Latin for onion) and Lilies are indeed related: Here are my sources, please site yours.

The bulbous onion (alliums) and its numerous relatives belong to the Lily family. Some of these alliums are distinctly ornamental; a few others, notably garlic, leek, Welsh onion, and chive, are common vegetables. All of the edible forms have related flavors and odors that are due principally to a volatile, irritating substance.

http://aggie-horticulture.tamu.edu/archives/parsons/publications/vegetabletravelers/onions.html

The Liliacea family includes such well-know edible, medicinal, and decorative plants as onions, leeks, garlic, chives, asparagus, yucca, agave, daylilies, tulips, amaryllis, hyacinths, daffodils, tiger lilies, Easter lilies, oriental lilies, camas lilies, dogtooth violets, fritillary, lily-of-the-valley, Solomon seal, trilliums, greenbriar, and aloes, including aloe vera.

http://www.susunweed.com/herbal_ezine/June09/healingwise.htm

Valued for its flavor, it may be cooked or eaten raw. The onion is an herb that belongs to the lily family. It is related to garlic, leeks, and chives. (onion | plant | Britannica.com)

Alliums belong to the Alliaceae - Lilium belong to the Liliaceae, so they are, in fact, entirely unrelated. Source - any reputable botanical or horticultural source, such as the RHS Encyclopaedia of Plants, or the Reader's Digest Encylopaedia of Plants and Flowers.

It's a sad fact that more and more inaccuracies are appearing on the internet and being presented as fact - its always best, these days, to seek out and check a proper horticultural or botanical source for accuracy.

Alliaceae is considered a sub-group of Liliaceae, but some consider it a separate family. I doubt it will be settled here. lol

You're probably right, it won't be;-))

UPDATE: But having done a quick check, you may have a point, because it appears that alliaceae is now included under the family Amaryllidacea, and is, indeed, listed as a sub group. Nonetheless, that still doesn't make Lilium and Allium related - it makes Amaryllis and daffodil and allium related, but Lilium are still members of the Lilaceae, a separate family. So it rather depends what a person means when they use the term 'lily' as to whether there's any relationship at all....

My source is the Kew Plant list and I think they are more reliable than most.

That's your opinion some would dispute.

Well, I think if you read through the list of plants included under Amaryllidacea, and in the sub group alliaceae, you will not find Lilium listed there. And if you google Liliaceae, lilium is there... but that's your choice to make, up to you.

None of this affects the planting time though does it?

Nope - unless the question, when it mentions lilies, doesn't mean hardy Lilium varieties.

My lilies don't care what time of year you stick them in the ground. I planted mine in the spring right after Easter. They are in bloom right now - you will see several pictures in my gallery. I kid you not. Same for my onions.

Steragram - I think in general you are correct :)

In the botanical world, Kew Gardens has the last word in plant taxonomy (scientific classification). This is mostly by scientific consensus, but they have to work at it , reviewing dozens of scientific articles a year, lately including many DNA studies.
Currently, the Allium is part of the Order Asparagales, while Lilium is part of the Order Liliales. So Alliums are more closely related to Asparagus than to Lilies! :)

Interesting Tug. Seems like it's been classified and re-classified by various schools of thought over time. Reminds me of the argument of whether Pluto is a planet of not. First it is, then no, then yes, then...?

Ah yes, the so called 'half life of facts', meaning half the things we know as 'fact' today will not be fact in the future... it can be difficult to keep up, and its not just in horticulture either!