Today when I was praying to God, I saw flower which was tucked to the left side of the photo (Lakshmi-venkateshwara) fell down. Is it a good or bad omen, if it is falling towards left side?
Flower falling while you pray itself is a good indication! Flowers are always considered very sacred, Goddess Laxmi is shown sitting on a lotus and her Favorite flowers are Lotus and any kind of Red Flowers.
While worshipping If a flower falls from the Picture or idol its a Good sign that your wish is going to fulfil and you will get success in your works. Left and right both sides are equally beneficial, Though in some places right side is considered more auspicious than left!!
Though, there is nothing to worry about as it's overall a good sign! You should keep that flower with you.