If you asked about Nickel Metal Hybrid batteries, the answer would be extremely easy. A large amount of studies have been done with these, usually concluding that they have lifespan comparable to those internal combustion engine vehicles. To cite the 100,000-Mile Evaluation of the Toyota RAV4 EV study,

The five-vehicle test is demonstrating the long-term durability of Nickel Metal Hydride batteries and of electric drive-trains. Only slight performance degradation has been observed to date with the highest mileage vehicles. Test data provide strong evidence that all five vehicles will exceed the 100,000-mile mark and SCE’s positive experience points to the very strong likelihood of a 130,000 to 150,000-mile battery and drive-train operational life. This is achieved by full or mostly full range use after every charge. EVs can therefore match or exceed the lifecycle miles of comparable internal combustion engine vehicles.

As such, the reduction of greenhouse gases is simply a net benefit for the environment. However, you asked for lithium-ion batteries. That makes the answer harder to answer. Lithium-ion batteries are used in hybrid cars since only very recently. Little information is available on the subject.

Don't take my word for it. It's the first thing said in the only peer-reviewed study I could find on the subject, published in August 2010:

Battery-powered electric cars (BEVs) play a key role in future mobility scenarios. However, little is known about the environmental impacts of the production, use and disposal of the lithium ion (Li-ion) battery. This makes it difficult to compare the environmental impacts of BEVs with those of internal combustion engine cars (ICEVs).

The study made several assumptions that were favorable to ICEVs:

Used a car more energy efficient than the average car sold in Europe in 2009. They used 5.2 L of gasoline per 100 km, instead of 5.7 L of diesel /100 km 6.6 L of gasoline /100 km.

"All expenditures for the exploitation of the lithium salts were allocated to the lithium salts, even though the saline brine yields other byproduct as well."

All the burden from production are allocated to the first life of each product even though the product might be reused or recycled. As explained in the study, this assumption heavily penalizes BEVs since recycling of electric batteries is high and since recycling of lithium is more energy efficient than production of it.

In spite of that, electric cars perform far better than conventional cars on all four indicators (abiotic depletion potential, global warming potential, cumulative energy demand, and eco-indicator 99):

In fact, the research concludes that

All the facts taken together, the results of the LCA, the various sensitivity analyses, the modeling applied for EOL, the assumption for the used electricity mix, etc., suggest that E-mobility is environmentally beneficial compared to conventional mobility. The Li-ion battery plays a minor role in the assessment of the environmental burden of E-Mobility. Thus, a Li-ion battery in an BEV does not lead to an overcompensation of the potential benefits of the higher efficiency of BEV compared to an ICEV.

They note, however, that it's not always necessarily always the case. A few very small and efficient internal combustion engine vehicles can perform as well as electric cars:

A break even analysis shows that an ICEV would need to consume less than 3.9 L/100km to cause lower CED than a BEV or less than 2.6 L/100km to cause a lower EI99 H/A score. Consumptions in this range are achieved by some small and very efficient diesel ICEVs, for example, from Ford and Volkswagen (13, 39).

They also note that the means by which the energy is produced influences the how environmentally-friendly BEVs are. The study used the average electricity production mix in Europe to give a general idea. If electricity comes from "an average hard coal power plant", the environmental burden is increased by 13.4%. On the other hand, if the electricity comes from hydropower plants, the environmental burden is decreased by 40.2%. As such, as countries move toward green energy, the environmental burden of electric cars will decrease.

The study does not address the cost of manufacturing the automobiles, but those costs are not significant. As a recent Argonne National Lab study concluded that, while hybrid cars cost more to produce, hybrid cars make up for their greater manufacture energy costs by being more environmentally-friendly on the road - especially if recycled materials are used in the vehicle's fabrication.

To cite the study's conclusion,