The LHCb experiment is one of the four large experiment of the Large Hadron Collider (LHC) situated at CERN, on the swiss-french border near Geneva. The LHCb detector is a single-arm spectrometer dedicated to the study of rare b-hadrons decays and to precision CP violation measurements. The LHCb experiment has so far collected 1fb–1 of data at a center of mass energy of 7TeV. This thesis addresses three topics related to the LHCb experiment. The first part concerns the alignment of the LHCb Inner Tracker with the first LHC data. Misalignments in the tracking system degrade the momentum measurement and flight distance determination of particles. Such quantities are vital for accurate lifetime and mass measurements. A standalone alignment of the Inner Tracker was performed using a method to stabilize the Inner Tracker alignment without the need of fixing elements. The Inner Tracker was aligned to a precision of 102 ± 10 µm, with a bias of 0 ±13 µm. In the second part, a first optimization of the selection cuts of the Same Side Kaon tagger has been performed using Ds+ → φπ+ 2010 data along with Bs0 Monte Carlo data. The Ds+ → φπ+ channel was shown to be suitable for this purpose in the absence of a large Bs0 calibration sample. Compared to the initial section of kaon, tuned on Monte Carlo data, an improvement both in tagging power and mistag rate was observed. In the third part, a method to fit the Bs0 lifetime in Bs0 → Ds–π+ and B0 lifetime in B0 → D–π+ was developed using a global decay time acceptance function and per-event decay time uncertainty estimates. The precision of the fits result is found to be dominated by systematic uncertainty due to the precision to which the acceptance function can be modeled. The average Bs0 lifetime is measured to be τBs0 = 1.515 ± 0.015(stat)-0.039+0.041 (sys) ps This result has an accuracy comparable to the world average provided by the Particle Data Group using Bs0 → DsX decays τBs0 = 1.425 ± 0.041 ps In the case of the B0, the average lifetime is measured to be τBd0 = 1.513 ± 0.020(stat)-0.037+0.033 (sys) ps It is expected that the precision of these measurements can be improved by using per-event acceptances in place of a global function.