Arabic joins its letters, and in most cases joining means adjusting a stroke so that one letter runs into the next. In one case it means something more: lam followed by alif is not written as a lam plus an alif but as a single mark, two strokes crossing in a narrow V or, in some hands, a rounded loop. The combination is obligatory. Writing the two letters separately is not an alternative style but an error, and the shape appears in every hand, from the earliest angular Kufic to modern print.
Because it is a single mark that stands for two letters, it sits awkwardly in the alphabet. Teaching charts often show it at the end of the twenty-eight as though it were a further letter, and beginners frequently learn it that way. It is not one. It has no name of its own beyond the names of its two parts, no numeral value of its own, and no place in the abjad sequence: for counting purposes it is a lam and an alif.
Other ligatures exist in the classical hands and there are a great many of them, but they are optional and belong to calligraphic practice rather than to spelling. A skilled scribe stacks certain sequences vertically, runs others together, and lengthens a connecting stroke to justify a line, and the repertoire of permitted combinations is part of what distinguishes one hand from another. Naskh uses few, thuluth uses many, and the hanging nastaliq of Persian and Urdu is built almost entirely out of them. Only lam and alif is required of everyone.