Samuel Taylor Coleridge said, “poetry = the best words in the best order”. Now lexicographers believe they know the best order for words, to put them in their dictionaries. So one could consider a lex poem to be one where the words are in lexicographic order. Then poets only have to choose the best words.
There are two ways that one can play this game. One is simply to write a poem in which the words are in dictionary order, like this:
A bold fanfare for his lex poem?
Quit, rather, reaching the very worst!
The other is to try to improve on an existing poem by sorting its words into dictionary order. Here is an example by e e cummings:
a a an arse everyone except
has is man politician sat upon which
If you don’t know the poem, you may enjoy trying to guess the sense of it, and then to re-sort the words into cummings’ order. There is a slightly serious purpose behind this: to investigate the amount of meaning in English text which is independent of word order.
A less demanding form is a poem whose lines are in dictionary order. In fact, this has already been done. In many books of poetry, especially anthologies, there is an “Index of first lines”. I remember seeing in the 1970s a poem which was simply a block of consecutive lines from such an index. Here is an example, from Q’s Oxford Book of English Verse:
Love bade me welcome; yet my soul drew back
Love guards the roses of thy lips
Love in fantastic triumph sate
Love in thy bosom like a bee
Love is a sickness full of woes
Love is and was my Lord and King
Love is enough: though the World be a-waning
Love is the blossom where there blows
Love not me for comely grace
Love, thou art absolute, sole Lord
Love wing’d my hopes and taught me how to fly
Lully, lulley; lully, lulley