How can I write an aligned environment with multiple anchor types?

Is it something like this you're after? I used alignedat to have full control on the columns spacing, and the optional [t] for the placement of the opening parenthesis, the closing being added at the end of the last line:

\documentclass{article}
\usepackage{amsmath, amssymb}

\begin{document}

\begin{gather}
\begin{aligned}
   &\text{lorem} + \text{ipsum} \\
= (&\begin{alignedat}[t]{3}
    &\text{dolor} &&+\text{sit} &&+\text{amet} \\
    &\text{consectetur} &&-\text{adipiscing} &&-\text{elit})
\end{alignedat} \\
= (&\begin{alignedat}[t]{2}
    &\text{sed} &&-\text{do} \\
    &\text{siusmod} &&+\text{tempor}).
\end{alignedat}
\end{aligned}
\end{gather}

\end{document} 

Here is an array solution, and a tabular* solution including equation numbers.

Note that \extracolsep does not apply before the first or after the last column.

\documentclass{article}
\usepackage{amsmath}
\usepackage{array}

\newcommand{\mytag}{\refstepcounter{equation}\llap{(\theequation)}}

\begin{document}

\begin{equation}
\begin{array}{rlll}
   & \text{lorem} + \text{ipsum} \\
 = (& \text{dolor}       &+\text{sit}        &+\text{amet} \\
   & \text{consectetur} &-\text{adipiscing} &-\text{elit}) \\
= (& \text{sed}     &-\text{do} \\
   & \text{siusmod} &+\text{tempor}).
\end{array}
\end{equation}

\noindent\begin{tabular*}{\textwidth}{@{}l% left margin, leave empty
  @{\extracolsep{\fill}}>{$\displaystyle}r<{$}
  @{\extracolsep{0pt}\hspace{2\tabcolsep}}>{$\displaystyle}l<{$}
  >{$\displaystyle}l<{$}
  >{$\displaystyle}l<{$}
  @{\extracolsep{\fill}}r@{}}
 &   & \text{lorem} + \text{ipsum} \\
 &= (& \text{dolor}       &+\text{sit}        &+\text{amet} \\
 &   & \text{consectetur} &-\text{adipiscing} &-\text{elit}) &\mytag \\
 &= (& \text{sed}     &-\text{do} \\
 &   & \text{siusmod} &+\text{tempor}). &&\mytag 
\end{tabular*}

\end{document}