This lesson relies a lot on humor and acting in order to show the students the difference between capital and lowercase letters, and it also requires you to be able to convert their Japanese names into English (correctly, not like how they show them in elementary school with the nonsense like ちゅ -> tyu and other such travesties). You'll need to ask the homeroom teachers for a class list far in advance so you have time to go through them all and write them out correctly.
Start the lesson off by telling the students about the types of letters in English. There are BIG letters (stand on your tip toes, motion big) and small letters (talk quietly, gesture teeny tiny). Write out each letter on the blackboard, and have students use their finger to trace the letter in the air as you write them. They should also say the letters while air tracing. Then, highlight difficult letters for Japanese people to distinguish (L and R, N and M, G and Z, B and V) and try to get them to pronounce them as differently as you can.
After the short introduction, use the homeroom teacher to demonstrate spelling. Make sure they know how to spell their name beforehand (especially for names with long vowels, eg Sato and not Satou), and then ask them how to spell their name, eg "How do you spell Tanaka?" As they're speaking, write their name in big letters on the blackboard, intentionally making mistakes with the capitalization by writing it in all caps. When they finish speaking, ask them, "Is this okay?" and make sure they answer "Yes." Then ask the class, "Is this okay?" When they all say okay, act very surprised and say "NOOO, this is NOT okay!" Then tell them that English names are BIG (loud voice, slow, pause for dramatic effect) small small small (quiet voice, faster). Erase the name on the blackboard and try again. Ask the homeroom teacher one more time, "How do you spell Tanaka?" This time, write it with correct capitalization as they are speaking. Ask them if it's okay, and then everyone say okay when all the capitalization is correct. Do this several more times, asking the homeroom teacher for the names of other school teachers (music teacher, science teacher, principal, etc), making sure you make mistakes with the capitalization each time, but changing where you make the mistake(s) each time. After each one, ask the students, "Is this okay?" If they say yes, act very surprised and angry and remind them BIG small small small. If they say no, ask them which letters have a mistake and fix them, finally writing the name correctly after they tell you.
After that demonstration, move onto the next activity: Balloon Man. This is just Hangman, but less (or possibly equally) gruesome. First, I pass out the English class lists (prepared beforehand), and tell the students that I'll use their names for this game. If you don't make and pass out the lists, you'll get a lot of students trying to use the incorrect Romanizations that no one uses and look terrible, but they're forced to learn in computer class for typing. So make sure they're looking at the correct Romanizations on a list you made. Then draw a stick figure on the board and attach some balloons to its head. Choose one student's name (first or last, switch between them for each question, but don't tell them which you're using), and draw that many blanks next to the stick figure. Ask for volunteers to guess a letter. If they guess correctly, write the letter(s) in the appropriate blank(s), making sure to make one or more capitalization mistakes for each name. If they're wrong, write the letter below the blanks and pop a balloon. Once they get all the letters, say hello to the student whose name you chose, and ask everyone, "Is this okay?" Usually by this time, they have forgotten to check for capitalization issues since it's a new activity, and they will tell you okay. Act surprised and mad and remind them BIG small small small (gestures). Then they should realize you're trying to trick them for this activity, too, and will probably correct you as you make the mistakes for the next questions. Use several students names, decreasing the amount of balloons you give them each time.
Finally, I pass out the personalized class word searches I made for them to do in the last 10-15 minutes of class. If they don't finish them, the rest is either homework or something the homeroom teacher can continue the next class when you're not there. This is personal information, and different for each class, so I can only post the template here, unfortunately. And since the point of this lesson is to highlight the difference between capital and lowercase letters, you can't use any of the numerous online word search generators, since those will spit out all caps or all lowercase. However, you can use tables in Word with invisible grid lines to a similar effect (see attachments), and make sure only the first letter of their names is capitalized. I find a 10x10 word search to be more than big enough for 3rd graders, and even smaller could be good if you don't have any names that require ten letters. I usually use their first names for the word search. The PowerPoint that I've posted here simply provides instructions for the word search, pointing out that they should look for the capital letters first, and then circle the rest of the name once they've found the capitals.