You can carefully slip a thin stake into the soil near the trunk to provide some support. Bamboo or metal stakes are nice since they are thin. Shouldn't hurt the tree provided you don't force it.

Hard to see from the picture but your tree does look like it's grafted and that you may have some growth coming from very near a possible graft line--you may wish to inspect closer to see if this is rootstock sucker growth, which generally should be removed. Other than that, it is reasonable to leave the new growth lower on the trunk unless you don't like the how it looks--citrus has a tendency towards a shrubby growth habitus. If you want it more of a standard arboreal form you can choose to prume off some of the lower new growth. And if you want to try to force some bushiness, you can also remove some of the top and tip growth, though I think that 1/3 is a bit too much to take off. If it were me, since the tree is still so young and thus without that much leaf surface area for photosynthesis as it is, I would consider waiting a bit in pruning off a large amount.

HTH.

It looks like root stock to me,too..I'd remove the bottom growth nearest the soil. You don't want root stock growing, otherwise it'll just take over. Toni