is the BCOUNT Autocad command available in LT 2011?
No.
Explore using QSELECT or FILTER commands to do about the same, in LT or full AutoCAD.
Usually when you select a windowed area (for instance) it will select all objects in the window and on the properties panel at the top it has a roll down that has the object selected list and reports how many lines, circles, blocks .... etc are in the selection set.
To take it a step further, if you use QSELECT and select a block it will find the instances of that block and report the quantity in the properties box roll down as well. I keep the properties box docked on the left side of my screen just for that purpose.
HTH
Regards,
DJ