In most years, with healthy ewes who have plenty of milk, and decent weather so you can get all families out within 24-36 hours tops, you would get away with freshening the pen between ewes a couple of times before needing to completely clear, lime and re-bed.
But the problem is that you usually don't know that it isn't going to be "most years" until you are in the middle of it, the weather is vile and you can't get ewes and lambs out; urine, birth fluids and spilled drinking water are spreading germs from pen to pen; the lambs start getting watery mouth because they are in pens which weren't disinfected and everyone has been in longer than expected... Yes, you are hearing a real life story here!!
So, as you are new to it and really don't want to be giving yourselves problems that could have been easily avoided, I would plan to have every ewe in a freshly-cleaned, limed and strawed pen. You might use a bit more straw and lime than you really needed, but you are much less likely to get problems - and if you do, you will know it was not through mismanagement or penny-pinching, but just that bad luck that befalls us all some years.
How many ewes are you talking, and what system? [Eg, lambing indoors, pen when lambed; lambing outdoors, only bring in families who need it; or what?)