Is it possible to do meta analysis of only two studies. What will be limitation of such analysis.
Yes, it is possible, but whether it is appropriate depends on the intent of your analysis.
Meta-analysis is a method of combining information from different sources, so it is technically possible to do a meta-analysis of only two studies - even of multiple results within a single paper. The key concern is not if you can do this, but that the method is appropriate for the questions that you have and the conclusions that you want to make, and that you acknowledgE the limitations of your analysis.
For example, the typical use of meta-analysis is to quantitatively synthesize previous studies on a particular subject, such as the effects of some medical intervention. In this context, it is important to make your criteria for study selection before the analysis and then find all studies available that meet those criteria. These criteria might limit the scope of your search to publications in English, in a particular journal or set of journals, those that use particular methods, etc. In practice, it is necessary to be familiar with the studies you are interested in to state these criteria. However, if you non-randomly select two papers from among many that have been published, it would introduce bias into your study. If only two studies have been published, it might be hard to justify any conclusions from a meta-analysis but it could still be done.
On the other hand, I have used the meta-analytical approach to synthesize data from a single study, for example if summary statistics are reported for subgroups but I am interested in finding the overall mean and variance. I don't always call this a meta-analysis in mixed company, so as not to confuse this application of the method with the more common use of meta-analysis as a comprehensive review sensu stricto.
If you compute a likelihood ratio for the effect of interest in each study, you can simply multiply them together to obtain the aggregate weight of evidence for the effect.