An alternative to using the SelectLayerByAttribute_management tool would be to create a SearchCursor on each featureclass that you are stepping through, in your case represented by the variable "stil". Use a whereclause on the cursor of "[Label] = 'diabase'". For each featureclass where the SearchCursor returns a row that is not equal to "None", this means the attribute was found, and you can add those to your list.
See the code below for an example:
import arcpy #Imports arcpy module which includes function info and license ifno
arcpy.env.workspace = "X:" #Set environment workspace to X: drive
ws = arcpy.ListWorkspaces("*","Folder") #Assigns list of folder type workspaces to variable "ws"
arcpy.env.overwriteOutput = True
dhList =  #Sets value of variable "dhList" to empty, thus defining as list variable
for w in ws: #Starts for loop, for each "w" workspace in "ws" workspace list set above
arcpy.env.workspace = w #Set arcpy environment to "w" folder workspace
gdb = arcpy.ListWorkspaces("*", "Access") #set variable "gdb" to list of Personal Geodatabases, which are MS Access databases, found in "w" workspace
for fc in gdb: #Starts for loop, Iterates through "fc" geodatabase in "gdb" list of PGDB workspaces
arcpy.env.workspace = fc #Again sets arcpy workspace to current geodatabase in For Loop
fcl = arcpy.ListDatasets("*", "Feature") #Set "fcl" variable to list of Feature datasets in current "fc" personal geodatabase
for fcc in fcl: #Starts for loop, iterate through each "fcc" feature dataset in "fcl" list of feature datasets
arcpy.env.workspace = fcc #Set arcpy workspace to current feature dataset in For Loop
fccl = arcpy.ListFeatureClasses("*", "All") #Set "fccl" variable to list of featureclasses contained in current "fcl" feature dataset
for stil in fccl: #Starts for loop, iterate through each "stil" featureclass in "fccl" list of feature classes
stilfields = arcpy.ListFields(stil) #Set "stilfields" variable to list of fields contained in current "stil" featureclass
for field in stilfields: #Starts For Loop, iterate through each "field" field in "stilfields" list of fields
fieldname = "Label" #Set "fieldname" variable to "Label"
if field.name == fieldname: #If 'Name' Property of "field" variable equals value of "fieldname" variable then do the following. Basically this tests to see if the featureclass contains a field named "Label"
newname = arcpy.AddFieldDelimiters(gdb,fieldname) #Starting to build SQL string to query value of "Label" field. Each geodatabase type requires different notation in the SQL String. this function adds the appropriate wrapper, whether single or double quotes or brackets to value of "fieldname" variable, based on the value of "gdb" variable, and assigns new string to "newname" variable.
attvalue = "diabase" #Set "attvalue" variable equal to string "diabase"
sqlstring = newname + " = " + attvalue #Set "sqlstring" variable equal to "newname" variable + equals sign + "attvalue" variable, creates string equal to "[Label] = 'diabase'"
fcrows = arcpy.SearchCursor(stil,sqlstring) #Sets "fcrows" variable equal to rows in "stil" featureclass that satisfy the "sqlstring" variable. So any rows that have a value in the "Label" field equal to "diabase" will be added to this list
fcrow = None #Set "fcrow" variable equal to None
fcrow = fcrows.next() #Set "fcrow" variable equal to the next value in the "fcrows" list variable
if not (fcrow == None): #Test to see if "fcrow" variable is NOT equal to None. If so, that means that "fcrows" list contained 1 or more values. This means that "stil" featureclass contained rows that matched your sql string.
dhList.append(stil) #Adds "stil" featureclass to "dhList" list, which we defined at the top of the script.
break #Breaks out of the For Loop going through the field list. If it reached this point, it means that it found the "Label" field and matched the attribute, so no need to look at further fields in this featureclass.
#At the bottom of each For statement, there is an implied Loop statement. So at the bottom of the code contained in the For statement, it will go back to the top, take the next value in the list and start over until there are no more values to evaluate, then it will move on to the next code block. For Loops are defined by indentations. Code below the For statement that is indented is inside the For Loop.
for item in dhList:
I am pretty basic with my coding skills, but this seems like it should do the trick.