Alternative to lying?

As per my understanding lying with any intention would break the fourth precept, whether its a white lie or not.

But instead of lying, I have heard that we can use Samyak Prayoga that would technically be a truthful statement, but deceive the listener, this basically like skipping the original question by providing a statement related to the question .

Other way may be bumping them back with a related question. Because when you are questioning someone that doesn't fall under the category of lies. For e.g. you can simply ask something like, Are you mad?, Oh, is that so? in which you don't lie or directly answer the question, but skipping the question letting the listener to go with his own assumptions.

If someone run past you and some chasing him with weapons ask you if you saw him or not

In this situation I may point to somewhere else other than the person actually went ( a direction slightly angled to the direction he actually went) and say I didn't see any one going to there(or this direction) or something similar to that which is technically not a lie.

If your boss call you and ask if one of your co-workers said something bad about the boss

In this case if the co-workers have ever told a good thing about the boss you can remind it. Oh, is that so? but I heard them talking that you are good in this with me, that day. Or if they haven't told any good about boss before, then you may say Oh, isn't it hard to believe that they told something like that about you?

However there may be situations you couldn't come up with a tricky answer/statement or you may be forced to answer exactly to the point. (Like if someone asked explicitly to say yes or no). Here the best option would be to remain silent, If you can't answer without lying, may be even though you had to sacrifice your life (I have heard of a Arhath thero who scarified his life by being silent to save a life of a bird (Kosava Lihini) which swallowed a gem in a jathaka katha) .

If in any case being silent is also not an option, my action would depend on the consequences. (Like king Dutugemunu who is suosed to be the Maithree Buddha decided to continue the war with the intention of preserving Buddhism, as the consequences of preserving Buddhism will be immense as unthinkable due to the many number of people who would find their path to Nirvana and it will out weight the bad merits gained by continuing war which took lives breaking the first precept.)

I don't really agree with replying using a riddle with the intention of deceiving or deluding the person you're talking to.

For example, instead of ...

Like saying i did not saw the man who ran away, thinking "There is no such being called me in reality, also there is no man who ran away in reality either"?

... you could just say "no" with the intention of openly lying, as described in this answer.

In a less extreme circumstance, (talking to your boss), if you don't want to say then don't say. You could reply something like, "I think it's better not to gossip." and optionally explain why (e.g. "because gossip gets taken out of context" and stuff about "confidentially" and "trust" and "team" and so on).

These situations require what is sometimes refereed to as skillful means

In your first example there are some possible replies, like in one Buddhist story a witness is called to the stand, and when asked a series of questions, he replied "I saw" "I did not see" to each of the questions. In such a way that no new information was added to the trial.

However what if the man with weapons turns on you, then you have a different problem.

So then what answer is neither lie nor an answer that might anger the man with the weapon towards you?

"I had dinner a few hours ago"

"I like your pants, where did you get them?"

"It sure is cloudy today"

These statements (assuming they are true at the time) avoid the truth that the weapon wielder seeks. Aside from the Bodhisattva vows there is nothing saying you have to answer a question when asked, and even there, there are provisions for being asked questions that might cause harm.

In the second situation you could say things like

"I don't feel comfortable having this conversation"

"You should ask them that not me"

or as ChrisW pointed out "I think it is better not to gossip"

If you say anything which is a lie it will give bad karma. So avoid lying at all times. If you have a situation where you have to tell a lie otherwise you hurt someone, you should be silent and say nothing. Saying nothing and keeping quiet is a great way to avoid telling lies.

If someone run past you and some chasing him with weapons ask you if you saw him or not, seeing the danger that he is in you might want to lie but if you do not lie he might get hurt.

While lying is deceit, if it saves a life, can that not be considered a wholesome act?

Recently while visiting one of the Sea Shepherd ships, I noticed a Buddhist statuette that was gifted from the Dalai Lama. While the sea shepherd ships stand between whales and other species that need their protection, the Dalai Lama himself is quoted as saying, in reference to Sea Shepherd tactics, 'when protecting life, it is not a [sin] to cause damage, as the life is more valuable'.

I would consider this to be in the same league as lying to someone who is going to cause serious injury or death. You are protecting life.

In Buddhist teachings it is the intention that is of utmost importance in may areas of life decisions.

If your boss call you and ask if one of your Co-workers said something bad about the boss, you will have to be truthful but in doing so you break a precept as you are using your word to make two people dislike each other.

This would be the equivalent of 'gossip' I would say. I have been put in this situation before and my answer was "the two of you need to sort your own business out and not involve others".

In these kind of situations can we imagine some other thing and answer thinking i'm answering in reference to my imagination and skip the breaking of precepts? Like saying i did not saw the man who ran away, thinking "There is no such being called me in reality, also there is no man who ran away in reality either"?

This would be very bad for you. At the end of the day your 'intention' is deception when you think this way. This can form a bad habit as you deceive yourself even more than you deceive the other people. As my example above, you don't have to lie, there are always other options.

For example, with the man chasing the other man, you could ask him instead "what is wrong" "can I help you", maybe he is chasing a man who hurt his child, or a robber. There are many options to be considered, and delving into the situation to gain better understanding would be better than deceiving yourself.

the answer is simple and it was offered in response to similar questions earlier

you cannot tell truth, you stay silent

maybe a white lie burdens with less black kamma than a malevolent or self-interested lie, but it's still a lie, so i see silence as the best strategy

It is common to desire not to tell a lie but at the same time to desire to answer a question and both desires can be very strong. However, the answer to a question is a statement, so what statement to make, if any? You can choose. This question is about control and influence. You perceive the opportunity to influence the action of another person by your own action of answering his question. But this is a conditioned and conventional response. In truth you have the opportunity to influence by your physical proximity, and always do. Other options are an attempt to disarm, a gift of money, a prayer, a quizzical look, to engage, or to ignore... the possibilities are endless!