Clipping raster by multiple datasets or polygons?

One thing I notice is that your third parameter is a hard coded output (C:/data/lidar). The way it's written now will loop through each of your features and overwrite the output every time, but since you may not have allowed the automatic overwriting of files, this could potentially be the hang-up. Try creating a unique output name for each iteration:

#creating a workspace and a list of feature classes
arcpy.env.workspace = "C:/data/lidar/lidar.gdb"
fcs = arcpy.ListFeatureClasses()

#looping through each feature class and creating a raster based on the extent of   
#feature class

i=0
for fc in fcs:
    outputPath = "C:/data/lidar" + str(i)
    i+=1
    arcpy.Clip_management("perth", "#", outputPath, fc, "", "ClippingGeometry")

Also, I'm not certain that you intended to place the outputs in the C:/data folder named lidar... note that the third parameter in clip is the full path of your output raster, not a folder that it will be placed in. If you don't specify an extension in your output path name and place them in a standard folder, it will be a grid, so right now your program is attempting to create a new grid dataset named 'lidar' in the C:/data folder.

Here are two options:

1. Use the built-in ArcGIS tool called Split Raster (Data Management).

   Divides a raster dataset into smaller pieces, by tiles or features from a polygon.

2. Try the Raster Split Tool, available from the USGS (see attached source code below).

Source code for USGS Raster Split tool:

"""
Raster Split Tool 6/16/2011
ArcGIS 10 Script Tool
Python 2.6.5

Contact:
Douglas A. Olsen
Geographer
Upper Midwest Environmental Sciences Center
U.S. Geological Survey
2630 Fanta Reed Road
La Crosse, Wisconsin 54603
Phone: 608.781.6333
"""
import arcpy
from arcpy import env
import os
from arcpy.sa import *

# Get Shapefile Name
inShape = arcpy.GetParameterAsText(0)
# Get Split Shapfile Name
splitShape = arcpy.GetParameterAsText(1)
# Get Field Name
splitField = arcpy.GetParameterAsText(2)
# Get Output Directory
outDirectory = arcpy.GetParameterAsText(3)
# Get Raster to Split
splitRaster = arcpy.GetParameterAsText(4)
# Get type of output tif, img, or GRID
rasterType = arcpy.GetParameterAsText(5)
# Set Workspace environment
env.workspace = outDirectory

# Run Split command on Input Shapefile
arcpy.Split_analysis(inShape, splitShape, splitField, outDirectory)

# Loop through a list of feature classes in the workspace
for fc in arcpy.ListFeatureClasses():
 
    # Execute ExtractByMask
    rfc = ExtractByMask(splitRaster, fc)

    # Clean up shp file from work directory
    arcpy.Delete_management(fc, "")    
    
    arcpy.AddMessage("Processing: " + fc)
    
    # Replace spaces with underscores
    fc = fc.replace(' ','_')
    
    # Remove .shp suffix
    fc = fc[:-4]
    
    # Trim to 13 chars
    fc = fc[0:13]
    
    if rasterType == 'img':
        fc = fc + "." + rasterType
    elif rasterType == 'tif':
        fc = fc + "." + rasterType
    else:
        print ('No extension')
        
    # Save the output
    rfc.save(fc)

for future seekers: Here's a modified version of the USGS raster split tool script that doesn't require anything above the ArcGIS Basic (ArcView) license level:

"""
Raster Split Tool 6/16/2011
ArcGIS 10 Script Tool
Python 2.6.5

Contact:
Douglas A. Olsen
Geographer
Upper Midwest Environmental Sciences Center
U.S. Geological Survey
2630 Fanta Reed Road
La Crosse, Wisconsin 54603
Phone: 608.781.6333

#####
modified 2015-04-15 by Jeremiah Poling ([email protected])
Now using only tools available at the ArcGIS Basic license level 
#####

"""
import arcpy
from arcpy import env
import os

# Get Split Shapfile Name
splitShape = arcpy.GetParameterAsText(0)
# Get Field Name
splitField = arcpy.GetParameterAsText(1)
# Get Output Directory
outDirectory = arcpy.GetParameterAsText(2)
# Get Raster to Split
splitRaster = arcpy.GetParameterAsText(3)
# Get type of output tif, img, or GRID
rasterType = arcpy.GetParameterAsText(4)
# Set Workspace environment
env.workspace = outDirectory

# Loop through the rows in the clipping shapefile
cursor = arcpy.SearchCursor(splitShape)
for row in cursor:
    resultName = row.getValue(splitField)

    # Create feature layer of current clipping polygon
    whereClause = '"' + splitField + '" = ' + "'" + resultName + "'"
    arcpy.MakeFeatureLayer_management(splitShape, 'currentMask', whereClause)

    # Replace spaces with underscores
    resultName = resultName.replace(' ','_')

    # Remove .shp suffix
    if resultName[-4:] == '.shp':
        resultName = resultName[:-4]

    arcpy.AddMessage("Processing: " + resultName)

    if rasterType == 'img':
        resultName = resultName + "." + rasterType
    elif rasterType == 'tif':
        resultName = resultName + "." + rasterType
    else:
        print ('No extension')

    # Save the clipped raster
    arcpy.Clip_management(
        in_raster = splitRaster,
        rectangle = "#",
        out_raster = resultName,
        in_template_dataset = 'currentMask',
        nodata_value="255",
        clipping_geometry="ClippingGeometry",
        maintain_clipping_extent="NO_MAINTAIN_EXTENT"
        )

    if arcpy.Exists('currentMask'):
        arcpy.Delete_management('currentMask')