I'm a new plant owner so bear with me! :) I got a lemon sprout in August from a close friend of mine. It was doing well for a few months, then it got cool and the sprout got a little droopy, so we figured it needed more light since we live in southern Illinois where temps are up and down all the time. It did wonders and the little guy really started to perk up. Then after a while the tips of the leaves started to turn yellow. I was looking through forums and found that it could be getting too much light or not enough nutrients or a number of things causing leaves to change color, but no pictures seemed to match mine. I changed the light schedule and it sprouted a second growth that shot way past the stalk with the yellowing leaves. This side is now much taller than the first, which has since stopped growing all together but still retains the exact same amount of yellowed tips. The newer "branch" is very tall now with many leaves and none of them seem to be yellowing. Is there a way to remedy this side of the tree? Should I snip it off? It started as the main part of the trunk but the newer branch has definitely taken over. In the picture below the left lower side is the yellowing leaves, the right taller piece is the new branch.

For a little bit of insight: I generally water as needed, filling the pot until the soil is saturated and barely dripping, then let it get to mostly dry in the soil for a few inches down before watering again. It gets light from the plant light for about 10-12 hours a day, which is moved often to act as "overcast," "sunny," and "cloudy" days.

thanks in advance!