Expanding a sequence inside a TikZ path

Here is a solution using \pgfextra, insert path and two custom keys:

\documentclass[tikz]{standalone}

\tikzset{
  recurse lattice path/.code args={#1#2}{
    \ifx#1.
    \else
    \ifx#1u
    \tikzset{insert path={-- ++(0,1) node[fill=black]{}}}
    \else
    \tikzset{insert path={-- ++(1,0) node[fill=black]{}}}
    \fi
    \tikzset{recurse lattice path=#2}
    \fi
  },
  lattice path/.code={%
    \draw (0,0) node[fill=black]{}
    \pgfextra{\tikzset{recurse lattice path={#1.}}};
  },
}

\begin{document}
\begin{tikzpicture}
  \tikzset{lattice path=rrurrur}
\end{tikzpicture}
\end{document}

Edit:

Here is a simpler solution without \pgfextra:

\documentclass[tikz]{standalone}

\tikzset{
  dep u/.style={insert path={-- ++(0,1) node{}}},
  dep r/.style={insert path={-- ++(1,0) node{}}},
  dep d/.style={insert path={-- ++(0,-1) node{}}},
  dep l/.style={insert path={-- ++(-1,0) node{}}},
  recurse lattice path/.code args={#1#2}{
    \ifx#1.\else\tikzset{dep #1,recurse lattice path=#2}\fi
  },
  lattice path/.style={recurse lattice path=#1.}
}

\begin{document}
\begin{tikzpicture}
  \tikzset{every node/.style={circle,fill,draw=none,inner sep=2pt}}
  \draw (0,0) node{} [lattice path=rrurrurrdddlll];
\end{tikzpicture}
\end{document}

Basically, you can't put a macro defined using \newcommand inside a TikZ path as it does a lot of stuff "under the covers" (e.g., \futurelet) which TikZ cannot handle.

You can, however, put arbitrary code inside \pgfextra{} in a TikZ path. In this case you could build the path inside \pgfextra and then insert it afterwards, like this:

\documentclass[tikz,border=0.125cm]{standalone}

\def\addtolatticepath#1{%
  \expandafter\def\expandafter\latticepath\expandafter{\latticepath#1}%
}

\def\latticepathletteru{\addtolatticepath{ -- ++(0,1) }}
\def\latticepathletterd{\addtolatticepath{ -- ++(0,-1) }}
\def\latticepathletterl{\addtolatticepath{ -- ++(-1,0) }}
\def\latticepathletterr{\addtolatticepath{ -- ++(1,0) }}

\def\parselatticepath#1{%
  \def\latticepath{node {}}%
  \Parselatticepath#1@}
\def\Parselatticepath#1{%
  \ifx#1@%
    \let\next=\relax%
  \else%
    \csname latticepathletter#1\endcsname%
    \addtolatticepath{ node {} }%
    \let\next=\Parselatticepath
  \fi%
  \next}

\tikzset{%
  insert lattice path/.style={%
    every node/.style={
      circle,
      fill,
      draw=none,
      inner sep=2pt
    },
    insert path={%
      \pgfextra{\parselatticepath{#1}}%
      \latticepath
    }
  }
}

\begin{document}
\begin{tikzpicture}
\draw (0,0) [insert lattice path={rrurruururuu}];
\end{tikzpicture}
\end{document}

This is an old question, but as I do not see a lot of answers here using parser PGF library, I add one.

\documentclass[tikz,border=7pt]{standalone}
\usepgfmodule{parser}

% macro that add #1 to the current path when used inside \pgfextra 
\def\insertpath#1{\tikzset{insert path={#1}}}
% define the parser "lattice path" 
\pgfparserdef{lattice path}{initial}{the letter u}{\insertpath{node{} -- ++(0,1) }}
\pgfparserdef{lattice path}{initial}{the letter r}{\insertpath{node{} -- ++(1,0) }}
\pgfparserdef{lattice path}{initial}{the letter d}{\insertpath{node{} -- ++(0,-1)}}
\pgfparserdef{lattice path}{initial}{the letter l}{\insertpath{node{} -- ++(-1,0)}}
\pgfparserdef{lattice path}{initial}{the character .}{\pgfparserswitch{final}}

\begin{document}
  \begin{tikzpicture}[every node/.style={circle,fill=red,inner sep=2pt}]
    \draw (0,0) \pgfextra{\pgfparserparse{lattice path}rrurrurrdddlll.} node{};
  \end{tikzpicture}
\end{document}