You can do this completely in model builder. To calculate the mean length, use Summary Statistics, as you described above. Do not specify a "case" field. The result of Summary Statistics will be a table containing a single row, with a field named "MEAN_LENGTH" or something similar.
Add a "Get Field Value" tool to the model (it's on the Modelbuilder toolbar, under Insert > Model Only Tools > Get Field Value). Use the summary statistics results table as your input table, and select the MEAN_LENGTH field. The output of this tool will be the value of MEAN_LENGTH, in a variable that you can then use in the rest of your model.