In Singapore, a registered trademark is valid for 10 years. Before the validity ends, the owner must renew the registration if he/she wants to keep ownership of the trademark. Once renewed, it is valid for a period of another 10 years. The same process is repeated if the owner still wants to keep hold of the mark years and years later.
Understanding how the term “lapse” is used in this question is crucial, so let’s start there. If you mean that the registered owner has not been using the mark within the 10-year period of validity, then no you still cannot use their trademark. As long as it’s within 10 years of the trademark’s registration, it is still protected under trademark law. For one, even if you argue that you don’t see the owner using it anymore, there are still a lot of ways he/she can prove otherwise. For example, if the owner has authorized a third-party firm to distribute products and services, that still means they are continuing their operations. Hence, they technically did not let the trademark lapse.
On the other hand, if by “lapse” you mean that the trademark registration has not been renewed, then you might have the chance to use the trademark. Not so fast though! Again, there are still a number of ways the former owner can reclaim the mark. If, for example, the trademark has established a positive reputation in the market, then it’s quite possible for the former owner to regain control of the trademark.
To sum it all up, if the trademark is not in use after the 10-year validity period, then anyone can have it registered. Even so, you need to do your research (like trademark searches) to make sure that the former owner really stopped using the mark. If you’re lucky enough, the former owner might have even ceased using the trademark long before the 10-year period ended.