Other way, you may ask why G+ bacteria lacks LPS but the G- ones have them? It is due to the unique physical properties of their individual cell walls, much as an added extra protective mechanism that evolved which confer greater stability of G- organisms against antibiotics, and more virulent pathogenicity. The origin of double membrane bacteria is a rich topic for research, and highly debated.
The reasons are both physiological and structural. Physiological in sense, they have evolved to counteract against environmental toxins or injuries which through evolution developed as a protective function (structural) that conferred greater stability to their existing cell wall structure. It is a variation in their cell wall structure, may by due to antibiotic selective pressure or other theories which are much debated.
A simple representation of their origin may be depicted as : monoderm bacteria → simple diderms lacking LPS → LPS containing archetypal diderm bacteria.
The unique cell wall structure of G+ve bacteria (monoderm) have PTG besides a single lipid membrane where it is structured as PTG-(CW-)-CM, or, a single unit membrane structure different than the G-ve ones.
In G-ve ones, it is OM(LPS)-PTG-ICM. The Gram stain that monoderms retain is due to the presence of a thick PTG. However, the intermediate ones stain positive due to the presence of PTG although they posses an outer cell membrane (lack LPS).
G-ve bacteria do have a thin layer of PTG sandwiched between the membranes as a component of their cell wall architecture. The reason that G+ PTG layer is thicker than the G- bacteria is due to evolutionary reasons that explains why most G- bacteria (diderms) show high resistance to antibiotics (although G+ bacteria also develop resistance). It is mostly a protective cellular barrier that evolved in G- ones when compared to the G+ bacteria.
The reason why G- bacteria have a much thicker periplasmic space when compared to the G+ ones also corresponds to the unique structure of their cell membranes which owes much to their evolutionary genetic repertoire against adverse environmental injuries.
You may try to derive some explanations from the study on the nature of origin and how evolution played part in the development of bacterial cell wall structures.
Sidharta covered the topic pretty well. If you would like a brief explanation, Silhavy et al. 2010 has an article entitled, "The Bacterial Cell Envelope" that did a nice job of laying of the key points on gram positive peptidoglycan thickness in the first paragraph under the gram positive section.
Silhavy et al. 2010: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2857177/
I want to mention that there is a big difference in the turgor pressure between G+ vs G- bacteria; the turgor pressures in G+ are about 15-20atm; meanwhile, in G- between 0.8 and 5atm (White's The physiology and biochemistry of prokaryotes 407p).