The motivation behind lazyWeave was to reproducible reports among those R users who hadn't yet learned LaTeX. It was, in my opinion, a noble goal, but happened to coincide with the wiser efforts behind the development of the knitr and rmarkdown packages. The development of these tools, which have become so common in the R community, have rendered most of the functionality of lazyWeave obsolete.
So at this point, we may ask, "why lazyWeave at all?" There are a handful of functions that I find quite useful still, and they can still be used in the rmarkdown documents. The functions you'll likely find most useful are:
lazy.matrixlazy.tablecattableconttablecatconttableuniv
All of these functions are capable of producing output in LaTeX, HTML, and RMarkdown.
lazyWeave is somewhat similar to the xtable package. What are the advantages of lazyWeave? To be honest, there really aren't a lot. In fact, xtable has quite a few more bells and whistles than lazy.matrix. For instance, with xtable you can turn column headings sideways, or use the longtable package in LaTeX. Eventually, I may add support for these features.
The only advantage lazy.matrix has over xtable is the ability to apply colors to the background of table rows.
The other advantage over xtable is the ability to define multicolumn cells (in LaTeX and HTML only) when building custom tables with lazy.table.
Beyond those basics, cattable, conttable, catconttable, and univ provide ready-made functionality for basic summaries with univariable comparisons. In fact, you may find that they are generally publication ready out of the box.