Employers often offer both options on company stock and grants of restricted stock as a reward and incentive to their employees. If stock is restricted, there are rules and restrictions for how employees can deal with the stock: when it will vest, when they can sell it, etc. Lapsed options are options that have expired.
Having an option on stock is different from owning shares of that stock. An option only gives the holder the right to buy stock at a fixed price at some point in the future. The great advantage of the option is the fixed price. Theoretically, all companies hope their stock will only continue to appreciate in price as time goes on. Therefore, the ability to buy stock in the future at the low, fixed price of the option would represent a gain to option holders, since it would allow them to purchase the stock for less-than-market price. But whatever happens, the value of stock options will depend greatly on fluctuations in the market price.
Most stock options come with a vesting period, a time during which the option holder must exercise the option (meaning, buy the stock the holder has a right to buy). The shares that the option holder has the right to buy are reserved during the vesting period. But if the holder fails to exercise, then the shares become available for the company to sell to other buyers or otherwise dispose of. When the option holder allows the option's vesting period to go by without exercising the right to buy, the option is said to have lapsed. There's no value in a lapsed option.
Restricted Stock Grants
Although stock options and restricted stock are two common components of employee reward programs, restricted stock is different from a stock option. Stock options can be openly tradable on the public market, but a restricted grant is given in a private offering and is often nontransferable. As the term "restricted" implies, the recipient of the stock doesn't simply own it free and clear; companies can set all sorts of conditions on ownership of restricted stock.
Restricted Stock Lapse
Restricted stock buyers may be able to pay for the stock immediately at a fixed, low price, but they often can't actually possess the stock until they meet requirements set by the company. For instance, employees are often given grants of restricted company stock, but they will not gain the rights to sell the stock until they've worked at the company for a certain number of years. The employee's ownership only vests when all restrictions imposed on ownership have been removed. This point is sometimes referred to as the "lapse" of restriction on the stock, but should not be confused with lapse of a stock option, which implies something very different.