Not lies but 'Toriah', if you search or ask a scholar what it is you ill know.
1- He looked up in stars and then said I am sick. It is to give his people an impression that he is seeking some knowledge from stars, while what he would mean is that he is sick because of their evil practices of star-worshipping etc.
2- He never said that the big idol had broken the others, he rather said بل فعله كبيرهم هذا, which mean 'but the bigger of them has done it.' This again is a metaphorical mention of himself because he is the one ho broke all the idols so he was the bigger of all of the idols in power.
3- Again as even mentioned in the narration, Ibrahim and Sarah were the only two believers on the whole land at that time, so what he said was correct that she was his sister in faith but the king understood the superficial meanings of his words.
On all three occasions he gave a statement which he intentionally worded that way that he did not lie, but left it for the listeners to give it their own meanings. Always remember that a true prophet of Allah would never lie as that would cast a dark shadow on every single word he would ever utter, if only once he is proved to have lied under any circumstances.
Wa Allah hu Aalam...