It's the usual problem: the package uses \roman for representing a counter value in roman numerals, but the greek option to babel changes \roman into a non fully expandable command.
Unfortunately, \roman is used in almost all macros of titlecaps, so providing a patch means rewriting the package.
The workaround suggested by Manuel in comments may work, but it can break Greek text.
\documentclass{article}
\makeatletter
\let\latex@roman\@roman
\makeatother
\usepackage[greek,british]{babel}
\usepackage{titlecaps}
\makeatletter
\let\@roman\latex@roman
\makeatother
\Addlcwords{of}
\begin{document}
This is some text.
\end{document}
As a side note: the titlecaps package needs to be revised anyway, because several of its macros have unprotected end-of-lines in the definitions.
A series of patches to the commands of titlecaps that should give the right behavior seems to be as follows:
\documentclass{article}
\usepackage[greek,british]{babel}
\usepackage{titlecaps}
\usepackage{xpatch}
\makeatletter
\def\dopatch#1{\xpatchcmd{#1}{\roman}{\romannumeral\value}{}{}}
\dopatch\Addlcwords
\dopatch\add@lcword
\dopatch\seek@lcwords
\dopatch\seek@lcwords
\dopatch\seek@lcwords
\dopatch\seek@lcwords
\dopatch\titlecap
\dopatch\titlecap
\dopatch\titlecap
\dopatch\titlecap
\dopatch\titlecap
\dopatch\titlecap
\dopatch\title@string
\dopatch\title@string
\dopatch\title@string
\dopatch\parse@@@Block
\undef\dopatch
\makeatother
\Addlcwords{of}
\begin{document}
This is some text.
\end{document}
In this way all occurrences of \roman{<counter>} are changed into \romannumeral\value{<counter>} which is safe, because it expands to \romannumeral\c@<counter> and the search for a number ends there.
Update
With titlecaps version 1.2, released 2015/01/30, the issues have been solved and your original example will work unchanged.
\romanfix, but I'm trying to understand his comment about unprotected end-of-lines. – Steven B. Segletes Jan 29 '15 at 01:56\land\aawhich had eluded me earlier. It may take a day or two to propagate. – Steven B. Segletes Jan 30 '15 at 11:40