They are not exactly rare. I think in Uncirculated Condition they are around $3 or $4, and in About Uncirculated condition probably around 20 cents. I'd still keep it as a lucky penny. Not every day you find one in the wild.
Welcome to coin Talk. The US Mint made more than 1 billion P Mint 1945 Lincoln cents. It's very common and would have to be a high grade mint state to have any value over one cent.
I suggest you only have a coin graded if you're gonna sell and make a big profit. The 1945, although it's a bit of a joy to find in change, it really is only worth one cent. That said, if you find a bronze/copper 1943 Lincoln cent piece, then spend the money to have it graded as that would be some big money!
All kidding aside Janika, we want to Welcome you to Coin Talk !! Keep searching, keep looking, and by all means, keep posting your finds, we love photos, and sooner or later, you will find something really nice !
Actually worth about 3 cents, more or less, for all it matters. Keep up the search! Good things will happen. Welcome to Coin Talk.
Welcome to CT. I love finding 74 year old coins (my birth year) in circulation and would keep all of them just because they are old and harder to find.