Place the anchovies into a pan over high heat and let the anchovies "melt" but not burn, whisking occasionally (they will pop and hiss and seem to "disappear") until they are good and broken up, about 3 minutes. Add the butter and lower the heat to medium, whisking gently to combine the butter as it melts into the anchovies. When the butter is completely melted, squeeze over the lemon juice-just to add a little bit of acid to it. Add the cream, whisking constantly to keep the sauce from breaking. (If it breaks, turn the heat to low, add a little bit of water and keep whisking; it should come right back together.)
Turn the heat to low, whisk another minute or so, and then remove from the heat until you need it. If you leave it on the back of the stove the ambient heat will keep it just fine, or you can set it aside and reheat at the last minute before using. Don't refrigerate; that will just put you in a world of hurt.