Home Shopping Network Inc. sued Drexel Burnham Lambert Inc. on Monday, accusing the investment firm of fraud in connection with its sale of $100 million in HSN convertible bonds to European investors last year. The shop-by-television retailer said in a suit filed in U.S. District Court in Tampa, Fla., that Drexel fraudulently induced Home Shopping to allow a new conversion price to be set for swapping the bonds for HSN stock. The suit also accused Drexel and the head of its high-yield investment bond group, Michael Milken, of secretly funneling the securities to its regular network of ``junk bond'' buyers and then acting in conjunction with the network to manipulate the HSN stock price downward during the 30-day period for setting the new conversion price. A Drexel spokesman, Steve Anreder, said the firm had not yet seen the lawsuit but ``it sounds like Home Shopping Network is unhappy with the market performance of its securities, over which we have no control.'' HSN's action comes against a background of a broad government inquiry into Drexel's operations that arose partly because of the firm's reported past business links with speculator and insider-trader Ivan F. Boesky, now serving a three-year prison term for securities fraud. Drexel has denied any improper activities and hasn't been charged with any wrongdoing. The HSN suit asked for invalidation of the price-reset provision in the bond sale and requested unspecified monetary damages for securities fraud, breach of fiduciary duty and other violations. HSN Chairman Roy Speer said that in addition to the lawsuit, the company filed a complaint with the Securities and Exchange Commission against Drexel and Milken charging them with manipulating HSN's stock. When the bonds were sold last April, they carried an original conversion price of $25.80 per share. At that price, the company would have had to issue about 3.9 million shares of stock to redeem all the bonds. But HSN said that after the bond offering was closed, it agreed at Drexel's request to include a provision to allow a new conversion price to be set at the 30-day average of HSN's share price prior to the April 22 conversion date plus a 20 percent premium. At the time of the bond issue, HSN was trading at about $18 a share on the American Stock Exchange, said Nando Di Filippo, HSN executive vice president. He said the stock had fallen to about $8 a share when the reset period started on March 10 and has fallen as low as $4.87{ a share since then. Although the reset period does not expire until Thursday, Di Filippo said it appears the conversion price will be about $6.50, which he said could result in the issuance of up to about 14 million shares of stock. That amount would not mean a change in control of the video retailer, but it would dilute the value of the company's outstanding stock, he said. Home Shopping, based in St. Petersburg, Fla., operates two television networks that offer items ranging from electronics equipment to jewelry for sale to viewers who call while the items are displayed. For the year ended Aug. 31, 1987, the company reported a profit of $29.5 million, or 33 cents per share, on sales of $582.1 million.