桔 (jú) as 'tangerine' is a simplified variant of 橘. Strictly, 桔 has another reading jié used in the plant name 桔梗 (bellflower). In practice, 桔 and 橘 are used interchangeably for tangerine.
Left tree radical - pictograph of a tree with branches and roots. It marks 桔 as a fruit-tree character; in mainland usage 桔 is the everyday simplified spelling for tangerine, sharing the slot with the more formal 橘. Same family: 林 forest, 桃 peach, 杏 apricot, 柳 willow.
Right 吉 supplies the sound - jí drifting to jú with a slight vowel shift. The lucky meaning is a happy coincidence: tangerines (桔) are New Year gifts in southern China precisely because the character contains 吉 "auspicious." Folk etymology reinforces the choice.
