user6219: I am working on some homemade lectures so I need good quality of sound, but unfortunately I do not have any budget so far(amateur stuff). 
I am looking for a camera that can shoot in Full HD and can have an external microphone attached. I do not need anything further than that, though.
I was considering SONY HDR-CX240 until I found out it cannot have external mic.
(What if it is a USB mic? It does have a USB slot.) So, should I quit this choice and buy a more expensive camera? Which one whould you recommend?
Is it possible that I record with the camera and external mic attached to my laptop at the same time?

user6219: Inspired by @Professor Sparkles♦'s answer, I decided to go for Samsung Galaxy S4* and a noise-reducing microphone with 3.5mm jack for Samsung (and other phones). I will keep you posted if this combination works well.
* I was offered Galaxy S4, S5 and LG G3 as the best video producing smartphones currently in the reseller's catalogue. My choice was based on desired quality\price trade-off.

user14478: If anyone is still looking for a similar setup that won't break the bank, I'd go with a laptop mounted cam - I have a Logitech HD Pro Webcam C920 which can be mounted on a tripod, too. The quality is amazing for the price (under $80), and I've used it to record lectures, demonstrations, as well as for recording and live streaming of some pretty unruly comedy and music shows. It has a stereo microphone that's really good (it made a crystal-clear recording of a live band in a noisy cafe from the back of the room), shoots well in low light, and has a decent zoom. It also does some onboard preprocessing, so HD recording won't overwhelm your laptop if it's an older/cheaper one.
With a tripod and a longer cable, you can do pretty much anything you'd do with a standard camcorder in a static situation. Depending on your software, you can attach an external mic to your laptop too, though I found the built-in mic of this cam superior to anything I've got.

user50: The Canon VIXIA HF R500 is the least expensive consumer camcorder (from a major brand) that I have been able to find. I own one and love it. It has an external microphone jack that is compatible with my wireless lapel mic receiver.
http://www.usa.canon.com/cusa/consumer/products/camcorders/consumer_camcorders/consumer_camcorders/vixia_hf_r500

user3295: Do you own a high-end smartphone? You can plug-in pretty much any microphone and have very decent audio quality. Some Android phones even support usb mics.
So you probably need a cheap adapter for standard stereo or mono mics to work with the 3 channel type headphone+mic jacks in modern phones. Something like this: https://www.amazon.com/StarTech-com-headsets-separate-headphone-microphone/dp/B004SP0WAQ/
It then only depends on the video quality of your phone. If that is satisfactory just get some sort of tripod adapter or other type of stand for phones and you're good to go. Definitely the cheapest solution if you already own a fitting phone.
If your phone is not an option I recommend you go with a webcam and USB microphone attached to your PC or Laptop. Most recording softwares have the option to choose a different audio source than your video recording device.
You can get a decent quality webcam for 20-30€ and a decent quality USB mic that can capture room audio for 15-20€.

6219: <p>I am working on some homemade lectures so I need good quality of sound, but unfortunately I do not have any budget so far(amateur stuff). </p>

<p>I am looking for a camera that can shoot in Full HD and can have an external microphone attached. I do not need anything further than that, though.</p>

<p>I was considering <code>SONY HDR-CX240</code> until I found out it cannot have external mic.
(What if it is a USB mic? It does have a USB slot.) So, should I quit this choice and buy a more expensive camera? Which one whould you recommend?</p>

<p>Is it possible that I record with the camera and external mic attached to my laptop at the same time?</p>
 6219: <p>Inspired by @Professor Sparkles♦'s answer, I decided to go for <code>Samsung Galaxy S4</code>* and a <a href="https://www.youtube.com/watch?v=fWjDl0e8YjQ" rel="nofollow">noise-reducing microphone with 3.5mm jack for Samsung (and other phones)</a>. I will keep you posted if this combination works well.</p>

<p>* I was offered <code>Galaxy S4, S5</code> and <code>LG G3</code> as the best video producing smartphones currently in the reseller's catalogue. My choice was based on desired quality\price trade-off.</p>
 14478: <p>If anyone is still looking for a similar setup that won't break the bank, I'd go with a laptop mounted cam - I have a Logitech HD Pro Webcam C920 which can be mounted on a tripod, too. The quality is amazing for the price (under $80), and I've used it to record lectures, demonstrations, as well as for recording and live streaming of some pretty unruly comedy and music shows. It has a stereo microphone that's really good (it made a crystal-clear recording of a live band in a noisy cafe from the back of the room), shoots well in low light, and has a decent zoom. It also does some onboard preprocessing, so HD recording won't overwhelm your laptop if it's an older/cheaper one.</p>

<p>With a tripod and a longer cable, you can do pretty much anything you'd do with a standard camcorder <em>in a static situation</em>. Depending on your software, you can attach an external mic to your laptop too, though I found the built-in mic of this cam superior to anything I've got.</p>
 50: <p>The Canon VIXIA HF R500 is the least expensive consumer camcorder (from a major brand) that I have been able to find. I own one and love it. It has an external microphone jack that is compatible with my wireless lapel mic receiver.</p>

<p><a href="http://www.usa.canon.com/cusa/consumer/products/camcorders/consumer_camcorders/consumer_camcorders/vixia_hf_r500" rel="nofollow">http://www.usa.canon.com/cusa/consumer/products/camcorders/consumer_camcorders/consumer_camcorders/vixia_hf_r500</a></p>
 3295: <p>Do you own a high-end smartphone? You can plug-in pretty much any microphone and have very decent audio quality. Some Android phones even support usb mics.
So you probably need a cheap adapter for standard stereo or mono mics to work with the 3 channel type headphone+mic jacks in modern phones. Something like this: <a href="http://rads.stackoverflow.com/amzn/click/B004SP0WAQ" rel="nofollow noreferrer">https://www.amazon.com/StarTech-com-headsets-separate-headphone-microphone/dp/B004SP0WAQ/</a></p>

<p>It then only depends on the video quality of your phone. If that is satisfactory just get some sort of tripod adapter or other type of stand for phones and you're good to go. Definitely the cheapest solution if you already own a fitting phone.</p>

<p>If your phone is not an option I recommend you go with a webcam and USB microphone attached to your PC or Laptop. Most recording softwares have the option to choose a different audio source than your video recording device.
You can get a decent quality webcam for 20-30€ and a decent quality USB mic that can capture room audio for 15-20€.</p>
