That the Bolsheviks managed to retain state power during these years - in the face of armed opposition, economic collapse, Allied intervention, etc - is pretty impressive. That they did so despite having no administrative or military experience, a set of deeply flawed politicial assumptions and a relatively narrow social base only makes the feat even more surprising. Contemporaries had good reason to assume that a Bolshevik government would collapse within weeks.
Yet what saved the Bolsheviks was a surprising degree of flexibility (as previewed in 1917) and state-building capacity (entirely unexpected). Lenin was central to the development of both new Soviet policy and state organisation.
Unfortunately at this point we need to pause for a caveat. Lenin was never a dictator like Stalin. While formal head of the Soviet government (Sovnarkom) and informal head of the Bolshevik/Communist Party, he did not and could not rule by fiat. In both state and party (the distinction is important) he was regularly challenged by his peers, often losing important votes (eg Brest-Litovsk). With that said, he was also the elder statesman of the party and had amassed an immense amount of political capital in 1917. Ultimately few would disagree with Bukharin when he admitted during the Left Communist dispute that:
Am I of sufficient stature to become leader of a party and declare war on Lenin and the Bolshevik Party? No, don't let us deceive ourselves.
The leading Bolsheviks were not by background suited to the task of administration. They were revolutionaries, exiles, poets, bandits and intellectuals. Almost none had any experience in management and they automatically felt more comfortable in the surroundings of political debating groups than formal government institutions. This is one reason why the party structures (Politburo, Central Committee, congresses, etc) remained places where policy could be discussed and argued over. Despite Lenin's efforts to move these deliberations to state bodies, the habit developed of agreeing key policy decisions in the Central Committee first and then transmitting them to Sovnarkom for implementation. Lenin was obviously involved in these discussions, and therefore a member of the small cohort (typically less than a dozen men) who decided general policy for the USSR. But, as noted above, while influential his voice was one amongst others.
But this was state policy, ie how to meet the many crises facing Soviet Russia at any one time. His theoretical writings largely ceased in favour of government work; the most significant exception, the national question, arose in the course of government work.
Beyond talking and theory, Lenin was also intimately involved in the detail of much of the above through Sovnarkom. Early Soviet state-building was ridiculously haphazard and chaotic, with bureaucratic duplication abounding. Lenin operated at the centre, as head of new new Soviet state, and sought to bring the various local bodies into some semblance of order. Specifically he served as Chairman of the Council of People's Commissars (Sovnarkom): while never able to usurp policy-making rights from the party, this body still commanded the new Soviet state and was responsible for implementing this policy.
This was a duty that Lenin took seriously. He was heavily involved in the day-to-day running of Sovnarkom meetings; initially meeting every day (although this slipped to once a week by 1921) he set agendas and actively chaired the meetings. This body was in theory the apex of the Soviet state, the key executive office. It was supported by the Little Sovnarkom, which dealt with more minor issues, and the the Labour and Defence Council (STO) which was an inner council concerned with with matters of urgency/importance to the Civil War. Lenin was the one individual to sit on all these bodies and no matter was too small for his attention - Simon Liberman recalls a session discussing the possibility of using pine cones as a revolutionary source of energy.
It was an impressive set-up, part borrowed from Tsarist practice and part innovative, that grew to become the heart of a functioning state apparatus. Not something that would have been necessarily predicted in 1917. But it was also a heavy load and Lenin's insistence on involving himself in bureaucratic minutiae almost certainly contributed to his early death.
But a functioning Soviet state was probably Lenin's greatest legacy from these years. October 1917 had seen him transform from theoretician to statesman and he was central to the Bolshevik ability to out-organise the Whites during the Civil War. Despite their own talents, few other leading Bolsheviks had his inclination towards administration and ability to read the political winds.
Obviously the Soviet state survived Lenin. Sovnarkom's importance had been largely due to Lenin's personal commitment to it and the political centre of gravity quickly shifted further back towards the party, with the state becoming a purely administrative tool. (Stalin didn't hold a formal role in the state apparatus until 1941.) But Lenin had played a key role in establishing the state's structure/capabilities and he was heavily involved in most of the key political questions of these years. The Soviet victory in the Civil War didn't come down to one man, and the Bolsheviks turned out to be surprisingly competent rulers survivors, but Lenin certainly made a significant contribution to the nature and direction of Soviet power.
Reading
For the nitty gritty of Lenin's experience in bureaucracy, see TH Rigby's Lenin's Government. James White runs a suitably critical rule over Lenin as statesman in Lenin: Theory and Practice of Revolution. Bukharin quote is from Stephen Cohen's Bukharin.