Summary
To plot the the moving (sliding) average use .MEAS,.PARAM and .STEP LTSpice directives (see the detailed explanation below). As a quick partial solution, use zoom in and Ctrl+Click on a plot title to show the average value (only a single value, not plot) for the selected abscissa range.
Solution. Plotting moving average for a signal
Suppose there is a following set-up and one needs to know the moving average of V(out):

Step 1: create the directive
Create the following SPICE directive (Edit -> Spice Directive):
.param t=0
.step param t 100n 900n 100n
.param S=100n
.meas tran Moving_Average avg(v(out)) TRIG time VAL=n-S/2 TARG time VAL=n+S/2
Comment for the directive:
1st line: define a time variable t.
2nd line: Step t from 100ns to 900 ns with the step 100ns.
3rd line: Set the moving average span: 100 ns.
4th line: Syntax:
Moving_Average - the name of the newly created variable to be calculated (put here whatever you like).
TRIG time VAL=t-S/2 - start of averaging.
TARG time VAL=t+S/2 - end of averaging.
E.g. if t=300 ns, averaging spans from 250 ns till 350 ns (300 +/- 100/2).
Step 2: run simulation, open the log file and plot the moving average
Run simulation
Open the Spice Error Log (View -> Spice Error Log), right click on any place and select Plot Stepped Measured Data

See the moving average plotted

Quick partial solution (see average value for a specified time range)
Suppose one has a chart like this:
And wishes to calculate an average value during [0.7us,0.8us].
Step 1: Specify the time range.
Double click on the abscissa axis and specify the needed range. Alternatively use Zoom to Rectangle tool (magnifier button in the top bar).
Step 2: Calculate the average
Ctrl + left mouse click on a chart title (bold green title V(out) in the picture) to see the average value for the specified range.
