I have already defined a node l1:

\node (l1) [ellipse, draw=black, fill=white!20, text=black, scale=0.8]{$l_1$};

And I would like to define another node l2 and position it with regard to l1. I know that below left=...cm of l1 exists, but what if I want to place l2 2cm below and 3cm left with regard to l1?


You can specify below left=<vertical distance> and <horizontal distance>. This will specify the distance between the node borders. If instead you want to specify the distance between the node centres, you can set on grid before below left=....

The positioning options are described on pp. 185 of the pgfmanual.




    every node/.style={
        ultra thick,
        outer sep=0pt % prevents the thick line from influencing the dimensions of the nodes
  \draw [gray!50] (-3,-2) grid (1,3); % to demonstrate placement
  \node (A) [ minimum width=2cm,minimum height=2cm] {A};
  \node [on grid, below left=1cm and 2 cm of A] (B) {B};
  \node [above left=1cm and 1cm of A] {C};


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