Fair Lanes Inc. posted a gain in profits in its third fiscal quarter ended March 31 to $2.5 million (57 cents a share) from $2.3 million (50 cents) for the same period last year. Sales were $23 million compared with $15.5 million last year.

Nine-month earnings were $4.3 million (99 cents), up from $3.9 million (86 cents) in the comparable period a year before. Sales were $61.4 million this year and $40.8 million through nine months of the 1981 fiscal year.

Silver Spring-based Computer Entry Systems Corp. has posted first-quarter profits of $383,000 (12 cents a share) compared with $280,000 (10 cents) in the same period last year. Sales were $2 million compared with $1.9 million last year.

The Federal Home Loan Mortgage Corp. , created by Congress in 1970, reported earnings of $30.9 million in 1981. The earnings were lower than 1981, but still produced the third best year in the corporation's history. Earnings in 1980 were 33.6 million.

The corporation was created to increase available funds for housing by developing and participating in a nationwide secondary market for conventional residential mortgages. To that end, it buys mortgage loans from institutions and resells them as mortgage pass-through securities to investors.

As of April 9, its 1982 purchase commitment volume was $7.1 billion, surpassing the total reported 1981 purchase comitment volume of $6.6 billion.

Systematic General Corporation reported earnings of $40,000 (3 cents) for the first quarter in 1982, contrasted with a loss of $75,000 (5.5 cents) in the first quarter of 1981. Sales were $3.763 million, up 12 percent from sales of $3.346 million in the first quarter of 1981.