You may be asking about the use of the lowercase letter ‘z’ in cursive italic handwriting, specifically what are appropriate joins into and out of the letter ‘z’ as in the word ‘lazy’.
As you can see from the examples on the webpage about cursive italic handwriting, the authors’ example joins out of ‘z’ but not into it.
The ease and legibility of italic handwriting comes from the fact that the print and cursive modes use the same letterforms. So, for example, the letter ‘z’ does not change from print to cursive, unlike other styles of cursive writing (see chart below for letter ‘Z’ from our Style Comparison resource).
The authors Getty and Dubay recommend no joins into ‘f’, or ‘z’ and no joins out of ‘g’, ‘j’ and ‘y’. This is because if you do, legibility will suffer — the extra lines will likely make it hard to read and/or awkward looking. See the example of ‘pizza’ below written in looped cursive, italic and italic with joins into ‘z’. We feel that line two (with the green check mark) is the most legible.
These recommendations not to join are standard practice for many variations of italic handwriting, and come from the 500-year history of the italic style.
However, it is your handwriting, so you are welcome to join wherever you wish — just remember to be extra careful with these joins, if you do make them. Also, these joins probably won’t make your handwriting faster. Research tells us* that students write faster when they pick up the pen sometimes instead of always connecting letters.
*Graham, S., Weintraub, N., & Berninger, V. W. (1998). The Relationship Between Handwriting Style and Speed and Legibility. The Journal of Educational Research, 91(5), 290–297. https://doi.org/10.1080/00220679809597556.
Font credit: Looped cursive example Learning Curve font; Italic examples with Getty-Dubay Joined font.