**Core Concept**
Lambda phage is a temperate bacteriophage that infects E. coli bacteria. It has a unique life cycle, exhibiting both lytic and lysogenic modes of replication.

**Why the Correct Answer is Right**
Lambda phage enters the host cell through a process called adsorption, where it attaches to the host cell's surface. Once inside, it injects its genetic material, a linear double-stranded DNA molecule, into the host cell's cytoplasm. The phage genome is then replicated, and the host cell's machinery is utilized to produce new phage particles. In the lysogenic mode, the phage genome integrates into the host cell's chromosome, forming a prophage that remains dormant until activated by certain environmental stimuli.

**Why Each Wrong Option is Incorrect**
**Option A:** Lambda phage does not use a viral envelope for entry into the host cell; instead, it relies on its tail fibers for attachment.
**Option B:** The correct replication process of lambda phage involves the host cell's machinery, not the phage's own replication machinery.
**Option C:** The lysogenic mode of lambda phage involves integration of the phage genome into the host cell's chromosome, not simply replication of the phage genome.

**Clinical Pearl / High-Yield Fact**
It's essential to note that bacteriophages like lambda phage can be used as vectors for gene therapy and vaccine development, taking advantage of their ability to infect and replicate within bacterial cells.

**Correct Answer: C. Lambda phage exhibits both lytic and lysogenic modes of replication.**