It is better for you to tell the truth than to cause upon a lie. Lying about your age is indeed forbidden, as is the principle with lying in general. So it is not permissible for you to evade this requirement in the surveys or websites. You should say the truth, if they accept it, then all the better, and if not, then the means to earn a lawful living are available for whoever seeks them. As such, you must respect their conditions and abide by them, as the Prophet Muhammad said,
“Reconciliation is allowable between Muslims except such as makes unlawful something which is lawful, or makes lawful something which is unlawful ; and Muslims must keep to the conditions they have made, except for a condition which makes unlawful something which is lawful, or makes lawful something which is unlawful.”
-Mishkat al-Masabih 2923
It is also confirmed that the Prophet said that whoever cheats is not one of us, as evident in the following hadith,
Narrated by Abu Hurairah:
That the Messenger of Allah (ﷺ) passed by a pile of food. He put his fingers in it and felt wetness. He said: 'O owner of the food! What is this ?' He replied: 'It was rained upon O Messenger of Allah.' He said: 'Why not put it on top of the food so the people can see it?' Then he said: 'Whoever cheats, he is not one of us.'"
-Jami` at-Tirmidhi 1315
You must always remember that we are not to lie, even if it might win us an advantage,
And do not be like she who untwisted her spun thread after it was strong [by] taking your oaths as [means of] deceit between you because one community is more plentiful [in number or wealth] than another community.1 Allah only tries you thereby. And He will surely make clear to you on the Day of Resurrection that over which you used to differ.
As such, lying is moreover a disease of the heart that only gets worse if left uncorrected,
In their hearts is disease, so Allah has increased their disease; and for them is a painful punishment because they [habitually] used to lie.
So He penalized them with hypocrisy in their hearts until the Day they will meet Him – because they failed Allah in what they promised Him and because they [habitually] used to lie.
Truly if you sin by knowing it is a sin, is indeed an act of abomination in the eyes of God.
“And We shall turn their hearts and their eyes away (from guidance), as they refused to believe therein for the first time, and We shall leave them in their trespass to wander blindly.”
Therefore, it is better not to lie about anything and to stay truthful, for such is an act of greatness in the eyes of the God, and the truthful will have a wonderous reward.
Allah will say, ‘This is the Day when the truthful will benefit from their truthfulness.’ For them are gardens [in Paradise] beneath which rivers flow, wherein they will abide forever, Allah being pleased with them, and they with Him. That is the great attainment.