Always squeeze lemons and limes into a cup or bowl, then remove the seeds and add juice to the recipe. If squeezed into the hand to let the juice run through the fingers, the possibility always exists that a seed will slip through too, unbeknownst to you, until one of your guests or yourself bites into it. You can squeeze into a small wire mesh strainer over a cup. That way you remove the seeds and strain with one action.
Soften pulp to facilitate squeezing by rolling whole lemon or lime firmly on counter top till you can feel the membranes inside break. Cut and squeeze.
To make squeezing easy, purchase a heavy duty lemon squeezer. When squeezing oranges, cut into 4 segments and place in bowl of squeezer pulp side down.