In LyX, how can I make the pages numbers start from the second page? (i.e., making the first page, which is the table of contents in my case, not having a page number on it)

Since LyX (up to recent version 2.0.x) only supports globally changing the pagestyle (in "Document > Setting... > Page Layout") using TeX code/ERT is a workaround.

If the first page should not be numbered then insert the TeX code/ERT

\thispagestyle{empty}


(To suppress page numbers for the whole TOC \pagestyle{empty} before TOC and \pagestyle{plain} after TOC can be used. Note that the last \pagestyle command on a page will take precedence over all \pagestyle commands on that page. Depending on your case another \thispagestyle{empty} after \pagestyle{plain} might be used.)
\setcounter{page}{1}