Should I be worried I missing my right lateral incisor tooth. What can I do to fill that gap?

Ask your Dentist. Tooth can be replaced or space can be closed orthodontically. See your dentist for restorative solutions, and ask your dentist for referral to orthodontic spesialist for examination (usually free). Best solution may be combination of both.
Yes. Aside from the way it looks to be missing a front tooth, which should be reason enough to replace it, the other surrounding teeth will move due to the void space. This will create spaces between other front teeth that won't look very good either. The best way to replace a front tooth is with an implant. A fixed bridge is another good option. Your dentist can advise you of your choices.
Missing tooth. You have several options ranging from a simple flipper to an implant and crown. Check out my website and you can see all the options available. jeff.